课程明细
Circuits Analysis
- 星期一，第 3—4 节，1—16 周，南校区博学楼 1J1B403；教学班：C电气251、C电气252。
- 星期三，第 1—2 节，1—16 周，南校区博学楼 1J1D317；教学班：C电气251、C电气252。
电工电子学A
- 星期一，第 5—6 节，1—12 周，南校区博学楼 1J1D410；教学班：C机制253、C机制254。
- 星期三，第 9—10 节，1—12 周，南校区博学楼 1J1C305；教学班：C机制253、C机制254。
- 星期五，第 5—6 节，1—12 周，南校区博学楼 1J1D410；教学班：C机制253、C机制254。
补充知识
- 什么是电阻： https://zhidao.baidu.com/daily/view?id=183681
- 电阻应用浅析： https://www.eet-china.com/mp/a416198.html
- 集总参数电路和分布参数电路： https://www.zhihu.com/question/320087308
作业
第一章作业
第1题
The charge flowing in a wire is plotted in Fig. 1.21. Sketch the corresponding current.
Fig. 1.21 — Charge waveform
第2题
The current entering the positive terminal of a device is $i(t)=3e^{-2t}\,\mathrm A$, and the voltage across the device is $v(t)=5\,di/dt\,\mathrm V$.
-
Find the charge delivered to the device between $t=0$ and $t=2\,\mathrm s$.
-
Calculate the power absorbed.
-
Determine the energy absorbed in 3 s.
第3题
Find the power absorbed by each of the elements in Fig. 1.26.
Fig. 1.26 — Element power (Problem 1.15)
第二章作业
第1题
Find the hot resistance of a lightbulb rated 60 W, 120 V.
第2题
Determine the number of branches and nodes in the circuit.
Branches and nodes
第3题
Calculate the power dissipated in the $5\,\Omega$ resistor in the circuit of Fig. 2.82.
Fig. 2.82 — Problem 2.18
第4题
Find $V_o$ in the circuit in Fig. 2.83 and the power dissipated by the controlled source.
Fig. 2.83 — Problem 2.19
第5题
Find the equivalent resistance at terminals $a$-$b$ for each of the networks in Fig. 2.99.
Fig. 2.99(a)
Fig. 2.99(b)
Fig. 2.99(c)
Fig. 2.99(d)
Fig. 2.99(e)
第6题
As a design engineer, you are asked to design a lighting system consisting of a 70-W power supply and two lightbulbs as shown in Fig. 2.118. You must select the two bulbs from the following three available bulbs.
- $R_1=80\,\Omega$, cost = $0.60 (standard size)
- $R_2=90\,\Omega$, cost = $0.90 (standard size)
- $R_3=100\,\Omega$, cost = $0.75 (nonstandard size)
The system should be designed for minimum cost such that $I=1.2\,\mathrm A\pm5\%$.
Fig. 2.118 — 70-W power supply and two lamps
第三章作业
第1题
For the circuit in Fig. 3.51, obtain $v_1$ and $v_2$.
Fig. 3.51
第2题
For the circuit in Fig. 3.66, find $v_1$ and $v_2$ using nodal analysis.
Fig. 3.66
第3题
For the bridge network in Fig. 3.76, find $i_o$ using mesh analysis.
Fig. 3.76
第4题
Find $v_x$ and $i_x$ in the circuit shown in Fig. 3.91.
Fig. 3.91
第四章作业
第1题
For the circuit in Fig. 4.73, assume $v_o=1\,\mathrm V$, and use linearity to find the actual value of $v_o$.
Fig. 4.73
第2题
Given the circuit in Fig. 4.75, calculate $i_x$ and the power dissipated by the $10\,\Omega$ resistor using superposition.
Fig. 4.75
第3题
Find $v_x$ in Fig. 4.83 by superposition.
Fig. 4.83
第4题
Obtain $v_o$ in the circuit of Fig. 4.87 using source transformation. Check your result using PSpice.
Fig. 4.87
第5题
Find the Thevenin equivalent at terminals $a$-$b$ of the circuit in Fig. 4.93.
Fig. 4.93
第6题
Determine the Thevenin and Norton equivalents at terminals $a$-$b$ of the circuit in Fig. 4.107.
Fig. 4.107
第7题
For the circuit in Fig. 4.117, what resistor connected across terminals $a$-$b$ will absorb maximum power from the circuit? What is that power?
Fig. 4.117
第六章作业
第1题
The voltage waveform in Fig. 6.46 is applied across a $30\,\mu\mathrm F$ capacitor. Draw the current waveform through it.
Fig. 6.46 — Capacitor voltage waveform
第2题
Find the voltage across the capacitors in the circuit of Fig. 6.49 under dc conditions.
Fig. 6.49
第3题
Determine the equivalent capacitance for each of the circuits in Fig. 6.51.
Fig. 6.51(a)
Fig. 6.51(b)
第4题
The current through a $5\,\mathrm{mH}$ inductor is shown in Fig. 6.66. Determine the voltage across the inductor at $t=1,3,\text{ and }5\,\mathrm{ms}$.
Fig. 6.66 — Inductor current waveform
第5题
Under DC conditions, find energy and voltage of capacitor and inductor.
Capacitor and inductor under DC conditions
第6题
Find $L_{\mathrm{eq}}$ at the terminals of the circuit in Fig. 6.75.
Fig. 6.75
第七章作业
第1题
The switch in Fig. 7.84 moves instantaneously from $A$ to $B$ at $t=0$. Find $v$ for $t>0$.
Fig. 7.84
第2题
The switch in Fig. 7.86 has been closed for a long time, and it opens at $t=0$. Find $v(t)$ for $t\ge0$.
Fig. 7.86
第3题
In the circuit of Fig. 7.93, $$v(t)=20e^{-10^3t}\,\mathrm V,\qquad t>0,$$ $$i(t)=4e^{-10^3t}\,\mathrm{mA},\qquad t>0.$$
-
Find $R$, $L$, and $\tau$.
-
Calculate the energy dissipated in the resistance for $0\lt t\lt0.5\,\mathrm{ms}$.
Fig. 7.93
第4题
Find $i(t)$ and $v(t)$ for $t>0$ in the circuit of Fig. 7.102 if $i(0)=10\,\mathrm A$.
Fig. 7.102
第5题
In the circuit of Fig. 7.99, find $i(t)$ for $t>0$ if $i(0)=2\,\mathrm A$.
Fig. 7.99
第九章作业
第1题
For the following pairs of sinusoids, determine which one leads and by how much.
-
$v(t)=10\cos(4t-60^\circ)$ and $i(t)=4\sin(4t+50^\circ)$.
-
$v_1(t)=4\cos(377t+10^\circ)$ and $v_2(t)=-20\cos377t$.
-
$x(t)=13\cos2t+5\sin2t$ and $y(t)=15\cos(2t-11.8^\circ)$.
第2题
Using phasors, find:
-
$3\cos(20t+10^\circ)-5\cos(20t-30^\circ)$
-
$40\sin50t+30\cos(50t-45^\circ)$
-
$20\sin400t+10\cos(400t+60^\circ)-5\sin(400t-20^\circ)$
第3题
Using phasors, determine $i(t)$ in the following equations:
-
$2\dfrac{di}{dt}+3i(t)=4\cos(2t-45^\circ)$
-
$10\int i\,dt+\dfrac{di}{dt}+6i(t)=5\cos(5t+22^\circ)$
第4题
Find current $i$ in the circuit of Fig. 9.42, when $v_s(t)=50\cos200t\,\mathrm V$.
Fig. 9.42
第5题
Find current $I_o$ in the circuit shown in Fig. 9.50.
Fig. 9.50
第6题
At $\omega=10^3\,\mathrm{rad/s}$, find the input admittance of each of the circuits in Fig. 9.74.
Fig. 9.74(a)
Fig. 9.74(b)
第十章作业
第1题
Determine $i$ in the circuit of Fig. 10.50.
Fig. 10.50
第2题
Determine $V_x$ in Fig. 10.55.
Fig. 10.55
第3题
Solve for $i_o$ in Fig. 10.73 using mesh analysis.
Fig. 10.73 — Problem 10.25
第4题
Find $i_o$ in the circuit shown in Fig. 10.85 using superposition.
Fig. 10.85 — Problem 10.40
第5题
Using source transformation, find $i$ in the circuit of Fig. 10.94.
Fig. 10.94 — Problem 10.49
第6题
For each of the circuits in Fig. 10.99, obtain Thevenin and Norton equivalent circuits at terminals $a$-$b$.
Fig. 10.99(a)
Fig. 10.99(b) — Problem 10.56
第十一章作业
第1题
Given the circuit in Fig. 11.35, find the average power supplied or absorbed by each element.
Fig. 11.35
第2题
In the circuit of Fig. 11.46, find the value of $Z_L$ that will absorb the maximum power and the value of the maximum power.
Fig. 11.46
第3题
For the power system in Fig. 11.67, find: (a) the average power, (b) the reactive power, (c) the power factor. Note that 220 V is an rms value.
Fig. 11.67
第4题
For the entire circuit in Fig. 11.70, calculate:
-
The power factor
-
The average power delivered by the source
-
The reactive power
-
The apparent power
-
The complex power
Fig. 11.70
第十二章作业
第1题
Obtain the line currents in the three-phase circuit of Fig. 12.42.
Fig. 12.42 — Three-phase Y–Y circuit
第2题
In the balanced three-phase Y–$\Delta$ system in Fig. 12.46, find the line current $I_L$ and the average power delivered to the load.
Fig. 12.46 — Problem 12.13
第3题
In Fig. 12.56, the rms value of the line voltage is 208 V. Find the average power delivered to the load.
Fig. 12.56 — Three-phase Y–Y circuit
第4题
Consider the $\Delta$–$\Delta$ system shown in Fig. 12.60. Take $Z_1=8+j6\,\Omega$, $Z_2=4.2-j2.2\,\Omega$, and $Z_3=10+j0\,\Omega$.
-
Find the phase currents $I_{AB}$, $I_{BC}$, and $I_{CA}$.
-
Calculate line currents $I_{aA}$, $I_{bB}$, and $I_{cC}$.
Fig. 12.60 — Chapter 12, Problem 51
第十三章作业 · Magnetically Coupled Circuits
Problem 13.1
For the three coupled coils in Fig. 13.72, calculate the total inductance.
Fig. 13.72 — Problem 13.1
Problem 13.4
(a) For the coupled coils in Fig. 13.74(a), show that $$L_{\mathrm{eq}}=L_1+L_2+2M.$$
(b) For the coupled coils in Fig. 13.74(b), show that $$L_{\mathrm{eq}}=\frac{L_1L_2-M^2}{L_1+L_2-2M}.$$
Fig. 13.74(a) — Problem 13.4
Fig. 13.74(b) — Problem 13.4
Problem 13.8
Find $v(t)$ for the circuit in Fig. 13.77.
Fig. 13.77 — Problem 13.8
Problem 13.10
Find $v_o$ in the circuit of Fig. 13.79.
Fig. 13.79 — Problem 13.10
Problem 13.15
Find the Norton equivalent for the circuit in Fig. 13.84 at terminals $a$-$b$.
Fig. 13.84 — Problem 13.15
Problem 13.36
As done in Fig. 13.32, obtain the relationships between terminal voltages and currents for each of the ideal transformers in Fig. 13.105.
Fig. 13.105(a) — Problem 13.36
Fig. 13.105(b) — Problem 13.36
Fig. 13.105(c) — Problem 13.36
Fig. 13.105(d) — Problem 13.36
Problem 13.41
Determine $I_1$ and $I_2$ in the circuit of Fig. 13.106.
Fig. 13.106 — Problem 13.41
Problem 13.45
For the circuit shown in Fig. 13.110, find the value of the average power absorbed by the $8\,\Omega$ resistor.
Fig. 13.110 — Problem 13.45
DC Circuit Test
For each circuit, find the downward load current $i_L$, the load voltage $u_L=V_b$, and the absorbed load power $P_L$. Use all six methods listed below. All elements are ideal; the bottom wire is ground (0 V).
Problem 1: Independent Sources Only
The $48\,\mathrm V$ source has a $4\,\Omega$ series resistor. At $b$, only the $2\,\mathrm A$ source and the $4\,\Omega$ load connect to ground.
Problem 2: With a Dependent Source
The $16\,\mathrm V$ source connects directly to $a$. The diamond is a dependent voltage source: $0.5v_x$, positive at the top, where $v_x=V_a$ is measured across the $4\,\Omega$ shunt at $a$.
Required methods for both problems
- Kirchhoff's current and voltage laws (KCL / KVL), with Ohm's law and branch-current equations;
- Superposition;
- Current-source and voltage-source transformations;
- Mesh-current analysis (a supermesh may be used);
- Nodal-voltage analysis;
- Thévenin's theorem at the load port ($b$ to ground).
State reference directions, draw necessary intermediate circuits, and show equations and calculations. Obtain $i_L$ by all six methods and verify agreement. For Thévenin's theorem, remove only $R_L$ to find $V_{\mathrm{Th}}$ and $R_{\mathrm{Th}}$, then reconnect it.
Notes
- For superposition, deactivate only the independent sources: short the ideal voltage source and open the ideal current source. Keep the dependent source active, and recalculate its control voltage in each subcircuit. Superpose currents or voltages, not powers.
- Preserve the control relation and source directions during source transformations. A dependent voltage source with a series resistor may also be transformed.
- To find $R_{\mathrm{Th}}$ with a dependent source present, deactivate the independent sources, retain the dependent source, and apply a port test source. Use $R_{\mathrm{Th}}=V_t/I_t$, with $I_t$ entering the original network.
第七版教材课后作业 / Seventh-edition Homework
16 章 · 每章 5 题 · 共 80 题 · 中等偏下
选自 Allan R. Hambley, Electrical Engineering: Principles and Applications, Seventh Edition, Global Edition（ISBN 978-1-292-22312-4）。保留教材题号；例后练习或改写题注明来源。英文题干附中文对照。优先选择电路分析、波形绘制与特性曲线题，61 道题配有图示，其余以基础计算和绘图为主。
请写出必要步骤、标明参考方向，计算结果注明单位。题图以 TikZ 重绘，连接关系、参考方向与数值依原版核对。页码为英文原书印刷页码。
第 1 章：绪论 / Introduction
本章 5 题 · Lower-intermediate
第 1 题 / P1.9 · Voltage, current, and energy direction
For the circuit element shown, $v=12\,\mathrm V$ and $i_{ba}=-2\,\mathrm A$. Find $v_{ba}$ with the correct algebraic sign and determine $i$. Is energy delivered to the element or taken from it?
中文对照
图 P1.9 所示电路元件有 $v=12\,\mathrm{V}$、$i_{ba}=-2\,\mathrm{A}$。求 $v_{ba}$ 的值并给出正确代数符号；求 $i$；判断能量传递给该元件还是由该元件发出。
第 2 题 / P1.21 · Element power
Calculate the power for each element shown. State whether each element absorbs or supplies energy.
中文对照
计算图 P1.21 中每个元件的功率，并分别判断元件吸收能量还是发出能量。
第 3 题 / P1.36 · Series elements and KCL
For Figure P1.36: (a) Which elements are in series? (b) What is the relationship between $i_d$ and $i_c$? (c) Given $i_a=3\,\mathrm A$ and $i_c=2\,\mathrm A$, determine $i_b$ and $i_d$.
中文对照
对图 P1.36：（a）哪些元件串联？（b）$i_d$ 与 $i_c$ 有何关系？（c）已知 $i_a=3\,\mathrm{A}$、$i_c=2\,\mathrm{A}$，求 $i_b$ 和 $i_d$。
第 4 题 / P1.42 · Kirchhoff's voltage law
Use KVL to find $v_a$, $v_b$, and $v_c$ in Figure P1.42.
中文对照
应用 KVL 求图 P1.42 中 $v_a$、$v_b$、$v_c$。
第 5 题 / P1.62 · Source and resistor power
Find $i_R$ through the resistor. Calculate the power of every element and identify the elements that absorb power.
中文对照
对图 P1.62，求流过电阻的电流 $i_R$，计算每个元件的功率，并指出吸收功率的元件。
第 2 章：电阻电路 / Resistive Circuits
本章 5 题 · Lower-intermediate
第 1 题 / P2.3 · Equivalent resistance
Find the equivalent resistance looking into terminals $a$ and $b$ of the network shown.
中文对照
求从图 P2.3 的端子 $a$、$b$ 看入的等效电阻。
第 2 题 / P2.24 · Series-parallel circuit analysis
Find $v_1$ and $v_2$ by combining resistances in series and parallel.
中文对照
通过合并串联和并联电阻，求图 P2.24 所示电路中的电压 $v_1$ 和 $v_2$。
第 3 题 / P2.36 · Voltage division
Use voltage division to calculate $v_1$, $v_2$, and $v_3$ in Figure P2.36.
中文对照
利用分压原理计算图 P2.36 中的 $v_1$、$v_2$ 和 $v_3$。
第 4 题 / P2.37 · Current division
Use current division to calculate $i_1$ and $i_2$ in Figure P2.37.
中文对照
利用分流原理计算图 P2.37 中的 $i_1$ 和 $i_2$。
第 5 题 / P2.80 · Thevenin and Norton equivalents
Find the Thevenin and Norton equivalents of the two-terminal circuit shown.
中文对照
求图 P2.80 所示二端电路的戴维南和诺顿等效电路。
第 3 章：电感与电容 / Inductance and Capacitance
本章 5 题 · Lower-intermediate
第 1 题 / P3.11 · Capacitor response to a current waveform
The current through a $0.5\,\mu\mathrm F$ capacitor is shown. The capacitor voltage is zero at $t=0$. Sketch the voltage, power, and stored energy to scale versus time.
中文对照
通过一个 $0.5\,\mu\mathrm{F}$ 电容器的电流如图 P3.11 所示，且 $t=0$ 时电压为零。按比例绘制电压、功率和储存能量随时间的波形。
第 2 题 / P3.24 · Equivalent capacitance
Find the equivalent capacitance of each circuit shown.
中文对照
求图 P3.24 所示各电路的等效电容。
第 3 题 / P3.45 · Inductor waveforms
The current through a $2\,\mathrm H$ inductor is shown in Figure P3.45. Sketch the voltage, power, and stored energy versus time.
中文对照
通过一个 $2\,\mathrm{H}$ 电感器的电流如图 P3.45 所示。绘制电压、功率和储存能量随时间的波形。
第 4 题 / P3.48 · Inductor response to a voltage waveform
The voltage across a $2\,\mathrm H$ inductor is shown. Its initial current is $i(0)=0$. Sketch the current, power, and stored energy to scale versus time.
中文对照
一个 $2\,\mathrm{H}$ 电感器两端的电压如图 P3.48 所示，初始电流 $i(0)=0$。按比例绘制电流、功率和储存能量随时间的波形。
第 5 题 / P3.51 · Inductor current ramp
A constant $20\,\mathrm V$ is applied to the $10\,\mu\mathrm H$ inductor shown. The initial current is $i_L(0)=-200\,\mathrm{mA}$. At what time $t_x$ does the current reach $+200\,\mathrm{mA}$?
中文对照
图 P3.51 所示 $10\,\mu\mathrm{H}$ 电感器两端施加恒定 $20\,\mathrm{V}$ 电压，且 $i_L(0)=-200\,\mathrm{mA}$。电流在何时 $t_x$ 达到 $+200\,\mathrm{mA}$？
第 4 章：暂态过程 / Transients
本章 5 题 · Lower-intermediate
第 1 题 / P4.3 · RC charging with an initial voltage
The capacitor initially has $v_C(0^+)=-20\,\mathrm V$. Find $v_C(t)$ and the time $t_0$ at which its voltage crosses zero. The component values and source voltage are shown.
中文对照
图 P4.3 所示电容器的初始电压为 $v_C(0^+)=-20\,\mathrm{V}$，其中 $R=50\,\mathrm{k\Omega}$、$C=0.04\,\mu\mathrm{F}$、$v_s=20\,\mathrm{V}$。求 $v_C(t)$ 的表达式，并求电压过零的时刻 $t_0$。
第 2 题 / P4.13 · Parallel RC transient
Derive $v_C(t)$ for the circuit shown and sketch it to scale versus time. The switch opens at $t=0$.
中文对照
图 P4.13 中，开关在 $t\lt 0$ 时闭合，在 $t=0$ 时断开。已知电流源为 $10\,\mathrm{mA}$，$R=2\,\mathrm{k\Omega}$、$C=10\,\mu\mathrm{F}$。推导 $v_C(t)$，并按比例作图。
第 3 题 / P4.21 · DC steady-state circuit
Find the steady-state values of $i_1$, $i_2$, and $i_3$ in the circuit shown.
中文对照
求图 P4.21 所示电路中 $i_1$、$i_2$ 和 $i_3$ 的稳态值。
第 4 题 / P4.23 · Capacitor switching response
The switch has been at A for a long time before $t=0$, when it moves to B. Find $v_R(t)$ and sketch it to scale for $-2\le t\le10\,\mathrm s$.
中文对照
图 P4.23 中，开关在 $t=0$ 前长期置于 A，$t=0$ 时切到 B。求 $v_R(t)$，并在 $-2\le t\le10\,\mathrm{s}$ 范围内按比例作图。
第 5 题 / P4.34 · First-order RL response
For Figure P4.34, $R=2\,\mathrm{k}\Omega$, $L=10\,\mathrm{mH}$, and the current source is $0.3\,\mathrm A$. The initial inductor current is $i_L(0^-)=-0.2\,\mathrm A$. Find $i_L(t)$ and $v(t)$ for $t\geq0$ and sketch them to scale versus time.
中文对照
图 P4.34 中 $R=2\,\mathrm{k\Omega}$、$L=10\,\mathrm{mH}$，电流源为 $0.3\,\mathrm{A}$，且 $i_L(0^-)=-0.2\,\mathrm{A}$。求 $t\ge0$ 时的 $i_L(t)$ 和 $v(t)$，并按比例作图。
第 5 章：正弦稳态分析 / Steady-State Sinusoidal Analysis
本章 5 题 · Lower-intermediate
第 1 题 / P5.21 · Phasor addition and phase relationships
Let $v_1(t)=50\cos(\omega t)$ and $v_2(t)=50\sin(\omega t)$. Use phasors to express $v_s(t)=v_1(t)+v_2(t)$ as a single term $V_m\cos(\omega t+\theta)$. Draw a phasor diagram showing $\mathbf V_1$, $\mathbf V_2$, and $\mathbf V_s$, and state the phase relationships between each pair.
中文对照
设 $ v_1(t)=50\cos(\omega t),\qquad v_2(t)=50\sin(\omega t). $ 利用相量把 $ v_s(t)=v_1(t)+v_2(t) $ 化为 $V_m\cos(\omega t+\theta)$ 形式的单项。画出显示 $\mathbf V_1$、$\mathbf V_2$ 和 $\mathbf V_s$ 的相量图，并说明每一对相量之间的相位关系。
第 2 题 / P5.33 · Inductor phasor and waveforms
The voltage $v_L(t)=10\cos(2000\pi t)$ is applied to a $200\,\mathrm{mH}$ inductor. Find its complex impedance and the voltage and current phasors. Draw a phasor diagram, write the current as a function of time, sketch voltage and current to scale, and state their phase relationship.
中文对照
将电压 $ v_L(t)=10\cos(2000\pi t) $ 加在 $200\,\mathrm{mH}$ 电感两端。求电感的复阻抗以及相量电压和相量电流，并画出相量图。写出电流的时域表达式，按比例画出电压和电流随时间变化的波形，并说明电流与电压之间的相位关系。
第 3 题 / P5.41 · Series RL phasor analysis
Find the current phasor and all voltage phasors for the circuit shown. Draw a phasor diagram showing $\mathbf V_s$, $\mathbf I$, $\mathbf V_R$, and $\mathbf V_L$. State the phase relationship between $\mathbf V_s$ and $\mathbf I$.
中文对照
求图 P5.41 所示电路的电流相量和各电压相量。画出显示 $\mathbf V_s$、$\mathbf I$、$\mathbf V_R$ 和 $\mathbf V_L$ 的相量图。$\mathbf V_s$ 与 $\mathbf I$ 之间有什么相位关系？
第 4 题 / P5.45 · Series RC phasor analysis
Find the current phasor and all voltage phasors for the circuit shown. Draw a phasor diagram showing $\mathbf V_s$, $\mathbf I$, $\mathbf V_R$, and $\mathbf V_C$. State the phase relationship between $\mathbf V_s$ and $\mathbf I$.
中文对照
求图 P5.45 所示电路的电流相量和各电压相量。画出显示 $\mathbf V_s$、$\mathbf I$、$\mathbf V_R$ 和 $\mathbf V_C$ 的相量图。$\mathbf V_s$ 与 $\mathbf I$ 之间有什么相位关系？
第 5 题 / P5.103 · Balanced three-phase Y–Y circuit
A balanced positive-sequence, $60\,\mathrm{Hz}$ wye-connected three-phase source has a line voltage of $440\,\mathrm{V_{rms}}$. It supplies a balanced wye-connected load with a $50\,\Omega$ resistor and a $0.3\,\mathrm H$ inductor in series in each phase. Find the line-to-neutral voltage phasors, line voltage phasors, line current phasors, and the active and reactive power delivered to the load. Take the phase of $\mathbf V_{an}$ to be zero.
中文对照
一个平衡正序星形连接的 $60\,\mathrm{Hz}$ 三相电源，其线电压为 $V_L=440\,\mathrm{V}_{\mathrm{rms}}$。该电源接到一个平衡星形连接负载，负载每相由 $0.3\,\mathrm{H}$ 电感与 $50\,\Omega$ 电阻串联组成。求线对中性点电压相量、线电压相量、线电流相量以及传递给负载的有功功率和无功功率。假设 $\mathbf V_{an}$ 的相角为零。
第 6 章：频率响应、伯特图与谐振 / Frequency Response, Bode Plots, and Resonance
本章 5 题 · Lower-intermediate
第 1 题 / P6.16 · Transfer function from waveforms
The input and output waveforms of a filter in sinusoidal steady state are shown. Determine the frequency and the corresponding complex value of its transfer function.
中文对照
根据图 P6.16 的稳态输入、输出波形，求频率及相应传递函数。
第 2 题 / P6.25 · RC low-pass filter output
The signal $v_{\mathrm{in}}(t)=5\cos(500\pi t)+10\cos(1000\pi t-30^\circ)+15\cos(2000\pi t+60^\circ)$ is applied to the low-pass RC filter shown. Find an expression for its output signal.
中文对照
图 P6.25 的低通 RC 滤波器输入为 $ v_{\mathrm{in}}(t)=5\cos(500\pi t) +10\cos(1000\pi t-30^\circ) +15\cos(2000\pi t+60^\circ). $ 计算各频率处传递函数并求输出。
第 3 题 / P6.30 · Bridge RC frequency response
Sketch $|H(f)|=|V_{\mathrm{out}}/V_{\mathrm{in}}|$ to scale versus frequency for the circuit shown. Find the half-power frequency. Hint: start with the Thevenin equivalent seen by the capacitor.
中文对照
对图 P6.30 电路，按比例绘制 $\lvert V_{\mathrm{out}}/V_{\mathrm{in}}\rvert$，并求半功率频率。提示：先求电容所见戴维南等效。
第 4 题 / P6.52 · First-order Bode plots
For $H(f)=100/[1+j(f/1000)]$, sketch the asymptotic magnitude and phase Bode plots to scale.
中文对照
对 $ H(f)=\frac{100}{1+j(f/1000)} $ 按比例绘制渐近幅值和相位伯特图。
第 5 题 / P6.72 · Series resonance
For the series resonant circuit shown, $L=20\,\mu\mathrm H$, $R=28.28\,\Omega$, and $C=1000\,\mathrm{pF}$. Calculate the resonant frequency, bandwidth, and half-power frequencies. At resonance, find the phasor voltage across each element and draw a phasor diagram.
中文对照
图 P6.72 有 $L=20\,\mathrm{\mu H}$、$R=28.28\,\mathrm{\Omega}$、$C=1000\,\mathrm{pF}$。求谐振频率、带宽、半功率频率；当源频率等于谐振频率时，求各元件电压相量并绘制相量图。
第 7 章：逻辑电路 / Logic Circuits
本章 5 题 · Lower-intermediate
第 1 题 / P7.27 · Logic circuits to Boolean expressions
Write a Boolean expression for the output of each logic circuit shown.
中文对照
为图 P7.27 所示各逻辑电路的输出写出布尔表达式。
第 2 题 / P7.46 · NAND implementation
Show how to implement the sum-of-products circuit shown using only NAND gates.
中文对照
说明如何只用与非门实现图 P7.46 所示的与项之和电路。图中输出为 $ AB+CD. $
第 3 题 / P7.55 · Karnaugh map
A logic circuit has inputs $A$, $B$, and $C$, and output $D=\prod M(1,3,5,7)$. (a) Construct the Karnaugh map for $D$. (b) Find a minimal sum-of-products expression. (c) Find a minimal product-of-sums expression.
中文对照
一个逻辑电路的输入为 $A$、$B$ 和 $C$，其输出为 $ D=\prod M(1,3,5,7). $ a. 构造 $D$ 的卡诺图。 b. 求最小与项之和表达式。 c. 求最小或项之积表达式。
第 4 题 / P7.81 · Shift-register state sequence
The initial state of the shift register shown is 100: $Q_0=1$, $Q_1=0$, and $Q_2=0$. Determine its subsequent states and the number of shifts required to return to the initial state.
中文对照
图 P7.81 所示移位寄存器的初始状态为 100，即 $Q_0=1, Q_1=0, Q_2=0$。求其后续各状态，并确定经过多少次移位后寄存器返回初始状态。
第 5 题 / P7.83 · Flip-flop timing waveforms
Both D flip-flops shown are positive-edge triggered. Assume $Q_0=Q_1=0$ before $t=0$. Sketch the voltage waveforms of $Q_0$ and $Q_1$ versus time, using logic levels of $0\,\mathrm V$ and $5\,\mathrm V$.
中文对照
图 P7.83 中的 D 触发器均为正边沿触发。设 $t=0$ 以前 $Q_0=Q_1=0$，画出 $Q_0$ 和 $Q_1$ 随时间变化的电压波形。逻辑电平取 $0\,\mathrm V$ 和 $5\,\mathrm V$。
第 8 章：计算机、微控制器与计算机化仪器系统 / Computers, Microcontrollers and Computer-Based Instrumentation Systems
本章 5 题 · Lower-intermediate
第 1 题 / P8.54 · Measurement accuracy
An instrumentation system measures distances from $0$ to $1\,\mathrm m$ full scale. Its accuracy is specified as $\pm0.5\%$ of full scale. If the measured value is $70\,\mathrm{cm}$, what is the possible range of the true value?
中文对照
某仪器系统测量的满量程距离范围为 $0$ 至 $1\,\mathrm{m}$，系统准确度规定为满量程的 $\pm0.5\%$。若测量值为 $70\,\mathrm{cm}$，真实值可能处于什么范围？
第 2 题 / P8.60 · Differential and common-mode signals
A differential amplifier has inputs $v_1(t)=0.005+5\cos(\omega t)$ and $v_2(t)=-0.005+5\cos(\omega t)$, in volts. Find the differential-mode and common-mode input voltages. Find the output for an ideal differential amplifier with differential gain $A_d=1000$.
中文对照
差分放大器的输入电压为 $ v_1(t)=0.005+5\cos(\omega t) $ 和 $ v_2(t)=-0.005+5\cos(\omega t). $ 求差模输入电压与共模输入电压。若差分放大器为理想放大器，且差模增益 $A_d=1000$，求放大器的输出电压。
第 3 题 / P8.68 · Sampling rate and ADC resolution
A computer-based instrumentation system uses a piezoelectric vibration sensor whose signal contains frequency components up to $30\,\mathrm{kHz}$. Specify the minimum sampling frequency. How many ADC bits are required for a resolution of $0.1\%$ of full scale or better?
中文对照
某计算机辅助仪器系统需要使用压电振动传感器的信号。已知该信号包含最高达 $30\,\mathrm{kHz}$ 的频率分量，应规定的最小采样频率是多少？若要求采样值的分辨率达到 ADC 满量程的 $0.1\%$ 或更好，ADC 至少应规定多少位？
第 4 题 / P8.70 · ADC resolution
An ADC must accept inputs from $0$ to $3\,\mathrm V$ and provide a resolution of $0.02\,\mathrm V$. What is the minimum number of bits required in its code words?
中文对照
需要一只输入电压范围为 $0$ 至 $3\,\mathrm{V}$、分辨率为 $0.02\,\mathrm{V}$ 的 ADC。码字至少需要多少位？
第 5 题 / P8.71 · Sampling and aliasing
A $10\,\mathrm{kHz}$ sinusoid is sampled at (a) $11\,\mathrm{kHz}$, (b) $8\,\mathrm{kHz}$, and (c) $40\,\mathrm{kHz}$. For each case, find the apparent frequency of the samples and determine whether aliasing occurs.
中文对照
对 $10\,\mathrm{kHz}$ 正弦波采样。分别求下列采样频率下采样值所呈现的表观频率，并判断是否发生混叠： (a) $11\,\mathrm{kHz}$； (b) $8\,\mathrm{kHz}$； (c) $40\,\mathrm{kHz}$。
第 9 章：二极管 / Diodes
本章 5 题 · Lower-intermediate
第 1 题 / P9.28 · Zener voltage regulator
In the regulator shown, $V_s$ varies from $10$ to $17\,\mathrm V$ and $i_L$ varies from $50$ to $200\,\mathrm{mA}$. Assume an ideal Zener diode. Find the largest allowable $R_s$ that keeps $v_L$ constant over these ranges, and the maximum power dissipated in $R_s$.
中文对照
图 P9.28 中 $V_s$ 在 $10$ 至 $17\,\mathrm V$ 间变化，$i_L$ 在 $50$ 至 $200\,\mathrm{mA}$ 间变化，稳压二极管理想。求使 $v_L$ 保持恒定时 $R_s$ 的最大允许值及 $R_s$ 的最大功率耗散。
第 2 题 / P9.36 · Ideal-diode circuit analysis
Find the indicated currents and voltages in each circuit shown, assuming ideal diodes.
中文对照
假定二极管理想，求图 P9.36 各电路中的 $I,V$。
第 3 题 / P9.41 · Diode output waveform
Sketch $v_o(t)$ to scale versus time for the circuit shown. Assume ideal diodes.
中文对照
假定二极管理想，按比例画出图 P9.41 中 $v_o(t)$ 随时间的波形。
第 4 题 / P9.50 · Half-wave rectification
A $20\,\mathrm{V_{rms}}$, $60\,\mathrm{Hz}$ AC source is in series with an ideal diode and a $100\,\Omega$ resistor. Find the peak current and the diode's peak inverse voltage (PIV).
中文对照
$20\,\mathrm{V_{rms}},60\,\mathrm{Hz}$ 交流源与理想二极管、$100\,\Omega$ 电阻串联，求峰值电流和二极管 PIV。
第 5 题 / P9.63 · Diode clipping waveform
Sketch the output waveform to scale for the circuit shown. Assume ideal diodes.
中文对照
假定二极管理想，按比例画出图 P9.63 的输出波形。
第 10 章：放大器的指标与外部特性 / Amplifiers: Specifications and External Characteristics
本章 5 题 · Lower-intermediate
第 1 题 / P10.4 · Measuring amplifier input resistance
The output voltage is $100\,\mathrm{mV}$ with the switch closed and $50\,\mathrm{mV}$ with the switch open. Find the amplifier input resistance.
中文对照
图 P10.4 中，开关闭合时输出电压 $v_o=100\,\mathrm{mV}$，开关断开时 $v_o=50\,\mathrm{mV}$。求放大器输入电阻。
第 2 题 / P10.5 · Amplifier gains
An amplifier driving a $100\,\Omega$ load has an input resistance of $200\,\Omega$ and a power gain of $5000$. Find its current gain and voltage gain.
中文对照
某放大器接 $100\,\mathrm{\Omega}$ 负载时，输入电阻为 $200\,\mathrm{\Omega}$，功率增益为 $5000$。求电流增益和电压增益。
第 3 题 / P10.9 · Output resistance
An amplifier has an open-circuit voltage gain of $100$. With a $10\,\mathrm{k}\Omega$ load, its voltage gain decreases to $80$. Find its output resistance.
中文对照
某放大器开路电压增益为 $100$，接入 $10\,\mathrm{k\Omega}$ 负载后电压增益降为 $80$。求输出电阻。
第 4 题 / P10.24 · Amplifier supply power
Find the net power delivered to the amplifier by the three DC supplies shown.
中文对照
求图 P10.24 中三个直流电源向放大器提供的净功率。
第 5 题 / P10.25 · Power and efficiency
Under high-signal test conditions, an audio amplifier supplies a $24\,\mathrm{V_{rms}}$, $1\,\mathrm{kHz}$ sinusoid to an $8\,\Omega$ load. Its power supply delivers $4\,\mathrm A$ at $50\,\mathrm V$. Neglect the input signal power. Find the efficiency and power dissipated in the amplifier.
中文对照
在大信号测试条件下，某音频放大器向 $8\,\mathrm{\Omega}$ 负载提供频率为 $1\,\mathrm{kHz}$、有效值为 $24\,\mathrm{V}$ 的正弦电压。电源以 $50\,\mathrm{V}$ 电压向放大器提供 $4\,\mathrm{A}$ 电流，信号源提供的信号功率可忽略。求效率和放大器耗散功率。
第 11 章：场效应晶体管 / Field-Effect Transistors
本章 5 题 · Lower-intermediate
第 1 题 / P11.27 · MOSFET bias point
Find $I_{DQ}$ and $V_{DSQ}$ for the circuit shown. The MOSFET has $V_{to}=1\,\mathrm V$ and $K=0.25\,\mathrm{mA}/\mathrm V^2$.
中文对照
求图 P11.27 所示电路的 $I_{DQ}$ 和 $V_{DSQ}$。MOSFET 的 $V_{to}=1\,\mathrm{V}$、$K=0.25\,\mathrm{mA}/\mathrm{V}^{2}$。
第 2 题 / P11.31 · MOSFET voltage-divider bias
(a) Find $I_{DQ}$ for the circuit shown, assuming $V_{to}=4\,\mathrm V$ and $K=1\,\mathrm{mA}/\mathrm V^2$. (b) Repeat for $V_{to}=2\,\mathrm V$ and $K=2\,\mathrm{mA}/\mathrm V^2$.
中文对照
（a）求图 P11.31 所示电路的 $I_{DQ}$，设 $V_{to}=4\,\mathrm{V}$、$K=1\,\mathrm{mA}/\mathrm{V}^{2}$；（b）令 $V_{to}=2\,\mathrm{V}$、$K=2\,\mathrm{mA}/\mathrm{V}^{2}$，重复计算。
第 3 题 / P11.50 · Common-source amplifier
For the common-source amplifier shown, the NMOS has $K_P=50\,\mu\mathrm A/\mathrm V^2$, $L=5\,\mu\mathrm m$, $W=500\,\mu\mathrm m$, $V_{to}=1\,\mathrm V$, and $r_d=\infty$. (a) Find $I_{DQ}$, $V_{DSQ}$, and $g_m$. (b) Find the voltage gain, input resistance, and output resistance, assuming the coupling capacitors are short circuits for AC.
中文对照
考虑图 P11.50 所示共源放大器。NMOS 参数为 $K_P=50\,\mu\mathrm{A}/\mathrm{V}^{2}$、$L=5\,\mu\mathrm{m}$、$W=500\,\mu\mathrm{m}$、$V_{to}=1\,\mathrm{V}$、$r_d=\infty$。（a）求 $I_{DQ}$、$V_{DSQ}$ 和 $g_m$；（b）假定耦合电容对交流信号短路，求电压增益、输入电阻和输出电阻。
第 4 题 / E11.9 · Common-source open-circuit voltage gain
For the common-source amplifier shown with the load disconnected, $g_m=1.77\,\mathrm{mS}$ and $r_d=\infty$. Treat the coupling and bypass capacitors as short circuits at midband. Find the open-circuit voltage gain $A_{voc}=v_o/v_{\mathrm{in}}$. Adapted from textbook Exercise 11.9 and Example 11.4, with transconductance supplied.
中文对照
图示共源极放大器的负载开路，已知 $g_m=1.77\,\mathrm{mS}$，$r_d=\infty$，中频时耦合与旁路电容可视为短路。求开路电压增益 $A_{voc}=v_o/v_{\mathrm{in}}$。本题根据教材练习 11.9 和例 11.4 改写，已给出跨导。
第 5 题 / P11.56 · Source follower analysis
For the source follower in Figure 11.26, $V_{DD}=15\,\mathrm V$, $R_L=2\,\mathrm{k}\Omega$, $R_1=1\,\mathrm M\Omega$, and $R_2=2\,\mathrm M\Omega$. The NMOS has $K_P=50\,\mu\mathrm A/\mathrm V^2$, $L=10\,\mu\mathrm m$, $W=160\,\mu\mathrm m$, $r_d=\infty$, and $V_{to}=1\,\mathrm V$. Find $R_S$ for $I_{DQ}=2\,\mathrm{mA}$, then calculate the voltage gain, input resistance, and output resistance.
中文对照
考虑图 11.26 所示源极跟随器，已知 $V_{DD}=15\,\mathrm{V}$、$R_L=2\,\mathrm{k}\Omega$、$R_1=1\,\mathrm{M}\Omega$、$R_2=2\,\mathrm{M}\Omega$。NMOS 参数为 $K_P=50\,\mu\mathrm{A}/\mathrm{V}^{2}$、$L=10\,\mu\mathrm{m}$、$W=160\,\mu\mathrm{m}$、$r_d=\infty$、$V_{to}=1\,\mathrm{V}$。求使 $I_{DQ}=2\,\mathrm{mA}$ 时的 $R_S$，再计算电压增益、输入电阻和输出电阻。
第 12 章：双极结型晶体管 / Bipolar Junction Transistors
本章 5 题 · Lower-intermediate
第 1 题 / P12.6 · BJT current gains
An NPN transistor has a forward-biased base-emitter junction and a reverse-biased base-collector junction. Given $i_C=16\,\mathrm{mA}$ and $i_B=0.4\,\mathrm{mA}$, calculate $i_E$, $\alpha$, and $\beta$.
中文对照
某 NPN 晶体管的发射结正向偏置、集电结反向偏置。已知 $i_C=16\,\mathrm{mA}$、$i_B=0.4\,\mathrm{mA}$，求 $i_E$、$\alpha$ 和 $\beta$。
第 2 题 / P12.49 · Single-transistor bias analysis
For the four-resistor bias circuit in Figure 12.22(a), $R_1=400\,\mathrm{k}\Omega$, $R_2=200\,\mathrm{k}\Omega$, $V_{CC}=15\,\mathrm V$, $R_C=10\,\mathrm{k}\Omega$, $R_E=10\,\mathrm{k}\Omega$, $\beta=100$, and $V_{BE}=0.7\,\mathrm V$. Find $I_{CQ}$ and $V_{CEQ}$.
中文对照
图 12.22(a) 的四电阻偏置网络取 $R_1=400\,\mathrm{k\Omega}$、$R_2=200\,\mathrm{k\Omega}$、$V_{CC}=15\,\mathrm{V}$、$R_C=10\,\mathrm{k\Omega}$、$R_E=10\,\mathrm{k\Omega}$、$\beta=100$、$V_{BE}=0.7\,\mathrm{V}$。求 $I_{CQ}$ 和 $V_{CEQ}$。
第 3 题 / P12.62 · Common-emitter amplifier analysis
For the common-emitter amplifier shown, draw the DC circuit and find $I_{CQ}$ and $r_\pi$. Calculate $A_v$, $A_{voc}$, $Z_{\mathrm{in}}$, $A_i$, $G$, and $Z_o$. Assume the coupling and bypass capacitors are short circuits at the operating frequency.
中文对照
对图 P12.62 的共射极放大器，画出直流电路并求 $I_{CQ}$，再求 $r_\pi$、$A_v$、$A_{voc}$、$Z_{\mathrm{in}}$、$A_i$、$G$ 和 $Z_o$。假设工作频率下耦合电容和旁路电容均可视为短路。
第 4 题 / P12.64 · Common-emitter amplifier with emitter degeneration
For the common-emitter amplifier shown: (a) Draw the small-signal equivalent circuit, assuming the coupling capacitors are short circuits. (b) Derive the voltage gain in terms of resistances, $r_\pi$, and $\beta$. (c) Derive the input resistance in the same terms. (d) For $\beta=100$, $V_{BEQ}=0.7\,\mathrm V$, $R_C=2\,\mathrm{k}\Omega$, $R_L=2\,\mathrm{k}\Omega$, $R_E=100\,\Omega$, and $V_{CC}=20\,\mathrm V$, find $R_B$ for $I_{CQ}=5\,\mathrm{mA}$. (e) Evaluate the gain and input resistance for these values.
中文对照
对图 P12.64 的共射极放大器：a. 假设耦合电容短路，画出小信号等效电路；b. 用电阻值、$r_\pi$ 和 $\beta$ 推导电压增益；c. 用电阻值、$r_\pi$ 和 $\beta$ 推导输入电阻；d. 设 $\beta=100$、$V_{BEQ}=0.7\,\mathrm{V}$、$R_C=2\,\mathrm{k\Omega}$、$R_L=2\,\mathrm{k\Omega}$、$R_E=100\,\Omega$、$V_{CC}=20\,\mathrm{V}$，求使 $I_{CQ}=5\,\mathrm{mA}$ 所需的 $R_B$；e. 对 d 中数值计算 b、c 所得表达式。
第 5 题 / P12.67 · Emitter-follower amplifier analysis
For the emitter-follower amplifier shown, draw the DC circuit and find $I_{CQ}$ and $r_\pi$. Calculate the midband values of $A_v$, $A_{voc}$, $Z_{\mathrm{in}}$, $A_i$, $G$, and $Z_o$.
中文对照
对图 P12.67 的射极跟随器，画出直流电路并求 $I_{CQ}$，再求 $r_\pi$ 以及中频段的 $A_v$、$A_{voc}$、$Z_{\mathrm{in}}$、$A_i$、$G$ 和 $Z_o$。
第 13 章：运算放大器 / Operational Amplifiers
本章 5 题 · Lower-intermediate
第 1 题 / P13.9 · Inverting amplifier waveforms
For the circuit in Figure P13.9, sketch $v_{\mathrm{in}}(t)$ and $v_o(t)$ to scale versus time. Assume the op amp is ideal.
中文对照
对图 P13.9，运放理想，按比例画出 $v_{\mathrm{in}}(t)$ 与 $v_o(t)$。
第 2 题 / P13.10 · Resistive-feedback amplifier gain
Determine the closed-loop voltage gain of the circuit shown, assuming an ideal op amp.
中文对照
求图 P13.10 的闭环电压增益。
第 3 题 / P13.16 · Op-amp currents and voltages
Assuming an ideal op amp, find all currents and voltages indicated in the inverting amplifier shown. KCL requires the total current entering a closed surface to equal the total current leaving it. Explain how this is satisfied for the dashed surface when a real op amp is used.
中文对照
对图 P13.16 的反相放大器，设运放理想，求图示各电流和电压。再说明实际运放下，穿过图示封闭面的电流如何满足 KCL。
第 4 题 / P13.20 · Ideal op-amp circuit calculations
For each circuit shown, assume an ideal op amp and find $v_o$. All circuits have negative feedback, so the summing-point constraint applies.
中文对照
对图 P13.20 的每个电路，设运放理想并求 $v_o$。各电路均为负反馈，故求和点约束适用。
第 5 题 / P13.22 · Removing the DC output component
The circuit shown has $v_{\mathrm{in}}(t)=4+3\cos(2000\pi t)$ in volts. Choose $R_2$ so that the DC component of $v_o(t)$ is zero, and find the resulting output voltage.
中文对照
图 P13.22 中 $ v_{\mathrm{in}}(t)=4+3\cos(2000\pi t). $ 选择 $R_2$，使 $v_o(t)$ 的直流分量为零，并求所得输出。
第 14 章：磁路与变压器 / Magnetic Circuits and Transformers
本章 5 题 · Lower-intermediate
第 1 题 / P14.12 · Flux and induced voltage
A uniform flux density of $2\,\mathrm T$ is perpendicular to a ten-turn circular coil of radius $20\,\mathrm{cm}$. Find the flux linking the coil and its flux linkages. If the field decreases uniformly to zero in $1\,\mathrm{ms}$, find the magnitude of the induced voltage.
中文对照
$2\,\mathrm T$ 的均匀磁通密度垂直穿过一个10匝、半径 $20\,\mathrm{cm}$ 的圆形线圈。求磁通和磁链。若磁场在 $1\,\mathrm{ms}$ 内匀速降至零，求感应电压的幅值。
第 2 题 / P14.43 · Inductance from magnetic reluctance
A 500-turn coil is wound on a core with magnetic reluctance $8\times10^5\,\mathrm{A\cdot turn/Wb}$. Find the inductance.
中文对照
一个500匝线圈绕在磁阻为 $8\times10^5\,\mathrm{A\cdot turn/Wb}$ 的铁芯上，求线圈电感。
第 3 题 / P14.44 · Coupled-coil transient
The coupled coils shown have $L_1=0.2\,\mathrm H$, $L_2=20\,\mathrm H$, and $M=2\,\mathrm H$. Both currents are zero before $t=0$. The switch closes at $t=0$. Find $i_1(t)$ and $v_2(t)$ and sketch them to scale versus time.
中文对照
图 P14.44 中 $L_1=0.2\,\mathrm H,L_2=20\,\mathrm H,M=2\,\mathrm H$，$t\lt 0$ 时电流均为零，$t=0$ 时开关闭合，左侧加 $10\,\mathrm V$，右侧开路。求 $i_1(t),v_2(t)$，并按比例作图。
第 4 题 / P14.64 · Ideal-transformer calculations
For the circuit shown, find the secondary rms voltage, secondary rms current, and load power for turns ratios $N_1/N_2=10$, $1$, and $0.1$.
中文对照
图 P14.64 中 $V_s=100\,\mathrm{V_{rms}}$、$R_L=100\,\Omega$。当 $N_1/N_2$ 分别为 $10,1,0.1$ 时，求 $V_{2\mathrm{rms}},I_{2\mathrm{rms}}$ 和负载功率。
第 5 题 / P14.69 · Reflected resistance and capacitance
Find the equivalent resistance $R'_L$ and capacitance $C'_L$ seen at the primary terminals of the transformers shown. Hint: impedance is reflected by the square of the turns ratio.
中文对照
求图 P14.69 中从变压器初级看入的等效电阻 $R'_L$ 和等效电容 $C'_L$。两变压器匝数比均为 $2:1$，负载分别为 $R_L=10\,\Omega$ 和 $C_L=1\,\mu\mathrm F$。（提示：按匝数比平方折算的是阻抗。）
第 15 章：直流电机 / DC Machines
本章 5 题 · Lower-intermediate
第 1 题 / P15.20 · Linear DC machine
When the switch in the linear DC machine shown closes, is the force on the sliding bar directed toward the top or bottom of the page? Find the initial starting force and the final bar velocity, neglecting friction.
中文对照
考虑图 P15.20 所示线性直流机。开关闭合后，导杆受力方向朝页面上方还是下方？求初始起动力的大小；忽略摩擦时，再求导杆最终速度。
第 2 题 / P15.29 · DC motor speed control
A DC motor drives a load requiring constant developed torque. With $V_T=200\,\mathrm V$, it runs at $800\,\mathrm{rpm}$ and draws armature current $I_A=15\,\mathrm A$. Its armature resistance is $3.0\,\Omega$, and the field current remains constant. Find the speed if $V_T$ increases to $250\,\mathrm V$.
中文对照
一台直流电动机驱动要求恒定电磁转矩的负载。当 $V_T=200\,\mathrm{V}$ 时，电动机以 $800\,\mathrm{rpm}$ 运行，$I_A=15\,\mathrm{A}$。已知 $R_A=3.0\,\Omega$，且励磁电流恒定。若 $V_T$ 增大到 $250\,\mathrm{V}$，求转速。
第 3 题 / P15.30 · DC motor power
A DC motor has $R_A=1.3\,\Omega$ and $I_A=15\,\mathrm A$. At $1000\,\mathrm{rpm}$ it produces back EMF $E_A=200\,\mathrm V$. Find the applied armature voltage, developed torque, and converted power.
中文对照
某直流电动机的 $R_A=1.3\,\Omega$、$I_A=15\,\mathrm{A}$，以 $1000\,\mathrm{rpm}$ 运行时产生反电动势 $E_A=200\,\mathrm{V}$。求电枢外加电压、电磁转矩和电磁转换功率。
第 4 题 / P15.31 · Separately excited DC motor
The motor shown runs at $1400\,\mathrm{rpm}$ with $R_F=150\,\Omega$, $V_F=V_T=200\,\mathrm V$, $I_A=15\,\mathrm A$, and $R_A=1.2\,\Omega$. Find $E_A$, $T_{\mathrm{dev}}$, $P_{\mathrm{dev}}$, and the total heat power dissipated in the resistances.
中文对照
图15.14所示电动机以 $1400\,\mathrm{rpm}$ 运行，$R_F=150\,\Omega$、$V_F=V_T=200\,\mathrm{V}$、$I_A=15\,\mathrm{A}$、$R_A=1.2\,\Omega$。求 $E_A$、$T_{\mathrm{dev}}$、$P_{\mathrm{dev}}$ 以及各电阻中转化为热的总功率。
第 5 题 / P15.68 · PWM speed control
A permanent-magnet motor supplied from $12\,\mathrm V$ has a no-load speed of $1700\,\mathrm{rpm}$. Neglect rotational losses. What average source voltage gives a no-load speed of $1000\,\mathrm{rpm}$? If the $12\,\mathrm V$ supply is chopped as shown, find the duty ratio $T_{\mathrm{on}}/T$.
中文对照
某永磁电动机由 $12\,\mathrm{V}$ 电源供电，无载转速为 $1700\,\mathrm{rpm}$。忽略旋转损耗。要使无载转速变为 $1000\,\mathrm{rpm}$，所需平均电源电压是多少？若按图15.25斩波 $12\,\mathrm{V}$ 电源，求占空比 $T_{\mathrm{on}}/T$。
第 16 章：交流电机 / AC Machines
本章 5 题 · Lower-intermediate
第 1 题 / P16.4 · Poles and slip
A $60\,\mathrm{Hz}$ induction motor must drive a load at approximately $850\,\mathrm{rpm}$. How many poles should it have? What is its slip at $850\,\mathrm{rpm}$?
中文对照
需要用一台 $60\,\mathrm{Hz}$ 感应电动机以约 $850\,\mathrm{r/min}$ 驱动负载。电动机应有多少极？当转速为 $850\,\mathrm{r/min}$ 时，转差率是多少？
第 2 题 / P16.10 · Slip and rotor frequency
A $10\,\mathrm{hp}$, six-pole, $60\,\mathrm{Hz}$ three-phase induction motor runs at $1160\,\mathrm{rpm}$ at full load. Find its slip and rotor-current frequency at full load. Also estimate its speed if the load torque is halved.
中文对照
一台 $10\,\mathrm{hp}$、六极、$60\,\mathrm{Hz}$ 三相感应电动机在满载时以 $1160\,\mathrm{r/min}$ 运行。求满载转差率和转子电流频率；并估算负载转矩减半时的转速。
第 3 题 / P16.21 · Induction motor efficiency
A $3\,\mathrm{hp}$, six-pole, $60\,\mathrm{Hz}$, delta-connected three-phase induction motor is rated at $1140\,\mathrm{rpm}$, $220\,\mathrm{V_{rms}}$, and $8.58\,\mathrm{A_{rms}}$ line current, with an $80\%$ lagging power factor. Find its full-load efficiency.
中文对照
一台 $3\,\mathrm{hp}$、六极、$60\,\mathrm{Hz}$ 三相三角形连接感应电动机的额定值为 $1140\,\mathrm{r/min}$、$220\,\mathrm{V_{rms}}$、$8.58\,\mathrm{A_{rms}}$（线电流），功率因数为 $80\%$（滞后）。求满载效率。
第 4 题 / P16.25 · Motor and load torque-speed curves
The curves shown belong to a $60\,\mathrm{Hz}$ induction motor and its load. How many poles does the motor have? Find the steady-state speed, slip, output power, and rotor copper loss. Neglect rotational losses.
中文对照
图 P16.25 给出一台 $60\,\mathrm{Hz}$ 感应电动机与负载的转矩—转速特性。该电动机有多少极？在稳态运行时，求转速、转差率、输出功率和转子铜损。忽略旋转损耗。
第 5 题 / P16.54 · Capacitor-start motor
The diagram gives the starting winding impedances of a $50\,\mathrm{Hz}$, $0.5\,\mathrm{hp}$ motor. Find the capacitance $C$ required to make the phase difference between $I_a$ and $I_m$ equal to $90^\circ$.
中文对照
图 P16.54 给出一台 $50\,\mathrm{Hz}$、$0.5\,\mathrm{hp}$ 电动机在起动条件下的绕组阻抗。求使电流 $I_a$ 与 $I_m$ 的相位差为 $90^\circ$ 所需的电容 $C$。
双语电工习题 / Electrical Engineering Exercises
Comprehensive Tests 1 and 2 contain 15 problems. Original problem numbers are retained. Show the necessary steps, clearly indicate reference directions, and include units in all numerical results.
综合测验1 / Comprehensive Test 1 (8 Problems)
Problem 1.1
Using the reference directions shown in the figure, determine the actual direction of the current and the power absorbed by the element. State whether the element absorbs or delivers energy.
Use the indicated reference directions to determine the actual current direction and the absorbed power.
Problem 1.2
Write the voltage–current relationship for each element shown below. State the DC steady-state equivalents of the inductor $L$ and capacitor $C$. For the dependent source, find the output current when $u_x=3\,\mathrm{V}$.
Use the source polarities and directions shown. For $R$, $L$, and $C$, use the passive sign convention: current enters the terminal marked positive.
The diamond represents a voltage-controlled current source.
Problem 1.3
For the loop circuit, use Kirchhoff’s voltage law (KVL) to find $I$ and the voltage across each resistor. For the node diagram, use Kirchhoff’s current law (KCL) to find $I_x$.
The upper terminal of the voltage source is positive. For each resistor, the terminal where the current enters is taken as positive.
Write the KCL equation using the current directions indicated by the arrows.
Problem 1.4
For the linear variations shown below, determine $u_L$ and $i_C$ using the passive sign convention.
Read the change in the plotted quantity and divide it by the corresponding time interval. Each sloping segment represents a constant rate of change.
Problem 1.5
Draw the circuit with each independent source acting alone. Use superposition to find $U_a$, then calculate the power dissipated by the $6\,\Omega$ resistor.
Use superposition to find the node voltage relative to ground, then calculate the power dissipated by the $6\,\Omega$ resistor.
Problem 1.6
Draw the circuits for the three steps: open-circuit the load terminals, determine the Thévenin resistance, and reconnect the load. Find $U_{\rm th}$, $R_{\rm th}$, $I_L$, and $U_L$.
Remove only the right-hand resistor $R_L$ as the load, and find the Thévenin equivalent of the remaining network.
Problem 1.7: RC Switching Transient — Three-Element Method
In the circuit below, switch $S$ has been in position 1 for a long time. At $t=0$, it moves from position 1 to position 2 and remains there. The source is $12\,\mathrm{V}$, $R_1=R_2=3\,\mathrm{k}\Omega$, $R_3=2\,\mathrm{k}\Omega$, and $C=100\,\mu\mathrm{F}$. The reference polarity of $u_C(t)$ is marked in the diagram. Assume ideal components and instantaneous switching.
The switch blade is shown in its pre-switch position. Only one fixed contact is connected at a time.
Find $u_C(t)$ for $t\ge0$ using the three-element method. Your solution must include:
- Determine the initial state from the circuit: With $S$ at position 1, draw the DC steady-state equivalent circuit for $t=0^-$. State how the capacitor is represented. Calculate the current through $R_1$ and $R_2$, and use the voltage across $R_2$ to find $u_C(0^-)$.
- Apply continuity: State the capacitor-voltage continuity condition and obtain $u_C(0^+)$.
- Find the final value: Redraw the circuit with $S$ at position 2 and determine $u_C(\infty)$.
- Find the time constant: Determine the resistance seen by the capacitor after switching and calculate $\tau$.
- Write the response: State the three-element response formula and substitute your values to obtain $u_C(t)$, including units. Check the initial and final values.
Problem 1.8: RL Switching Transient — Three-Element Method
In the circuit below, switch $S$ has been open for a long time, and the circuit is in DC steady state. At $t=0$, $S$ closes and remains closed, bypassing $R_2$. The $12\,\mathrm{V}$ source remains connected, and the inductor branch is never opened. The component values are $R_1=4\,\Omega$, $R_2=8\,\Omega$, and $L=0.6\,\mathrm{H}$. Treat the switch and inductor as ideal. The reference direction of $i_L(t)$ is downward, as shown.
The switch is shown open, its pre-switch state. Closing $S$ changes the circuit resistance while preserving a continuous path for the inductor current.
Find $i_L(t)$ for $t\ge0$ using the three-element method. Your solution must include:
- Determine the initial state from the circuit: With $S$ open, draw the DC steady-state equivalent circuit for $t=0^-$. State how the ideal inductor is represented. Identify the resistors in the current path and calculate $i_L(0^-)$ from the source voltage and total resistance.
- Apply continuity: State the inductor-current continuity condition and obtain $i_L(0^+)$.
- Find the final value: Redraw the circuit with $S$ closed. Identify which resistor is bypassed and determine $i_L(\infty)$.
- Find the time constant: Keep $S$ closed, deactivate the independent voltage source, and determine the resistance seen by the inductor. Calculate $\tau$.
- Write the response: State the three-element response formula and substitute your values to obtain $i_L(t)$, including units. Check the initial and final values.
综合测验2 / Comprehensive Test 2 (7 Problems)
Problem 2.1
Express the complex number $z=1+\mathrm{j}\sqrt3$ shown in the figure in trigonometric, exponential, and polar forms. Express $2\angle(-90^\circ)$ in rectangular form. Specify the unit used for the angle in the exponential form.
Read the real and imaginary parts from the complex plane, then determine the magnitude and argument.
Problem 2.2
Evaluate the following four expressions:
- $(2+\mathrm{j}3)+(1-\mathrm{j})$
- $(2+\mathrm{j}3)-(1-\mathrm{j})$
- $(1+\mathrm{j})(1-\mathrm{j})$
- $(4+\mathrm{j}2)/(1+\mathrm{j})$
Problem 2.3
Given $u(t)=12\sqrt2\cos(1000t-30^\circ)\,\mathrm{V}$, state its RMS value, amplitude, and angular frequency, and write both the RMS and peak-value voltage phasors. If the current phase angle is $-60^\circ$, determine the phase relationship between the voltage and current.
Compare only the angles. The arrow lengths do not represent the relative magnitudes of the voltage and current in this problem.
Problem 2.4
Find $Z$, $\dot I$, $U_R$, and $U_L$. Draw the impedance-equivalent circuit and the voltage triangle, using the current as the phase reference.
Series RL circuit: $X_L$ is the inductive reactance at the specified frequency.
Problem 2.5
Find $Z$, $\dot I$, $P$, and $Q$. Draw the voltage triangle and state whether the current leads or lags the source voltage.
Series RC circuit: $X_C$ is the positive magnitude of the capacitive reactance; the capacitor impedance is $-\mathrm{j} X_C$.
Problem 2.6
Find the total impedance, the RMS source voltage, the complex power, the apparent power, and the power factor. Draw the impedance, voltage, and power triangles, labeling all values and units.
Series RLC circuit: I denotes the RMS current.
Problem 2.7: Balanced Three-Phase Star and Delta Loads
An ideal balanced three-phase, three-wire source has a frequency of $50\,\mathrm{Hz}$ and an RMS line-to-line voltage of $U_{\mathrm{L}}=380\,\mathrm{V}$. Three identical load impedances, each $Z=8+\mathrm{j}6\,\Omega$ at this frequency, are connected first in star (Y) and then in delta ($\Delta$), as shown below. The source voltage and each load impedance remain unchanged. Neglect the impedance of the supply conductors. The star point $N$ is isolated (no neutral conductor).
(a) Star (Y) connection: $Z_{AN}=Z_{BN}=Z_{CN}=8+\mathrm{j}6\,\Omega$.
(b) Delta ($\Delta$) connection: $Z_{AB}=Z_{BC}=Z_{CA}=8+\mathrm{j}6\,\Omega$.
For each connection, determine:
- The RMS voltage across each load impedance, $U_{\mathrm{ph}}$, and the RMS phase current $I_{\mathrm{ph}}$ (the current through each load impedance).
- The RMS line current $I_{\mathrm{L}}$ in each supply conductor, $A$, $B$, and $C$.
- The active power absorbed by each phase: $P_{AN}$, $P_{BN}$, and $P_{CN}$ for the star load; $P_{AB}$, $P_{BC}$, and $P_{CA}$ for the delta load.
- The total three-phase active power $P_{\mathrm{total}}$.
Show the line-to-phase voltage and current relationships used in each case. Give current magnitudes in amperes and active powers in watts or kilowatts. Round numerical results to three significant figures.
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