• Home
  • Textbooks
  • Introductory Circuit Analysis
  • Series and Parallel ac Circuits

Introductory Circuit Analysis

Robert L. Boylestad

Chapter 15

Series and Parallel ac Circuits - all with Video Answers

Educators

Chapter Questions

Problem 1

Express the impedances in Fig. 15.120 in both polar and rectangular forms.
a. (FIGURE CAN'T COPY)
b. (FIGURE CAN'T COPY)
c. (FIGURE CAN'T COPY)
d. (FIGURE CAN'T COPY)
e. (FIGURE CAN'T COPY)
f. (FIGURE CAN'T COPY)

Check back soon!

Problem 2

Find the current $i$ for the elements in Fig. 15.121 using complex algebra. Sketch the waveforms for $v$ and $i$ on the same set of axes.
a. (FIGURE CAN'T COPY)
b. (FIGURE CAN'T COPY)
c. (FIGURE CAN'T COPY)
d. (FIGURE CAN'T COPY)
e. (FIGURE CAN'T COPY)
f. (FIGURE CAN'T COPY)

Check back soon!

Problem 3

Find the voltage $v$ for the elements in Fig. 15.122 using complex algebra. Sketch the waveforms of $v$ and $i$ on the same set of axes.
a. (FIGURE CAN'T COPY)
b. (FIGURE CAN'T COPY)
c. (FIGURE CAN'T COPY)

Check back soon!

Problem 4

Calculate the total impedance of the circuits in Fig. 15.123. Express your answer in rectangular and polar forms, and draw the impedance diagram.
a. (FIGURE CAN'T COPY)
b. (FIGURE CAN'T COPY)
c. (FIGURE CAN'T COPY)

Check back soon!

Problem 5

Calculate the total impedance of the circuits in Fig. 15.124. Express your answer in rectangular and polar forms, and draw the impedance diagram.
a. (FIGURE CAN'T COPY)
b. (FIGURE CAN'T COPY)
c. (FIGURE CAN'T COPY)

Check back soon!
09:18

Problem 6

Find the type and impedance in ohms of the series circuit elements that must be in the closed container in Fig. 15.125 for the indicated voltages and currents to exist at the input terminals. (Find the simplest series circuit that will satisfy the indicated conditions.)
a. (FIGURE CAN'T COPY)
b. (FIGURE CAN'T COPY)
c. (FIGURE CAN'T COPY)

Yaqub Khan
Yaqub Khan
Numerade Educator
14:13

Problem 7

For the circuit in Fig. 15.126:
a. Find the total impedance $\mathbf{Z}_T$ in polar form.
b. Draw the impedance diagram.
c. Find the current $\mathbf{I}$ and the voltages $\mathbf{V}_R$ and $\mathbf{V}_L$ in phasor form.
d. Draw the phasor diagram of the voltages $\mathbf{E}, \mathbf{V}_R$, and $\mathbf{V}_L$, and the current $\mathbf{I}$.
e. Verify Kirchhoff's voltage law around the closed loop.
f. Find the average power delivered to the circuit.
g. Find the power factor of the circuit, and indicate whether it is leading or lagging.
h. Find the sinusoidal expressions for the voltages and current if the frequency is $60 \mathrm{~Hz}$.
i. Plot the waveforms for the voltages and current on the same set of axes.
(FIGURE CAN'T COPY)

Linda Winkler
Linda Winkler
Numerade Educator

Problem 8

Repeat Problem 7 for the circuit in Fig. 15.127, replacing $\mathbf{V}_L$ with $\mathbf{V}_C$ in parts (c) and (d).
(FIGURE CAN'T COPY)

Check back soon!

Problem 9

Given the network in Fig. 15.128:
a. Determine $\mathbf{Z}_T$.
b. Find $\mathbf{I}$.
c. Calculate $\mathbf{V}_R$ and $\mathbf{V}_C$.
d. Find $P$ and $F_p$.
(FIGURE CAN'T COPY)

Check back soon!
14:13

Problem 10

For the circuit in Fig. 15.129:
a. Find the total impedance $\mathbf{Z}_T$ in polar form.
b. Draw the impedance diagram.
c. Find the value of $C$ in microfarads and $L$ in henries.
d. Find the current $\mathbf{I}$ and the voltages $\mathbf{V}_R, \mathbf{V}_L$, and $\mathbf{V}_C$ in phasor form.
e. Draw the phasor diagram of the voltages $\mathbf{E}, \mathbf{V}_R, \mathbf{V}_L$, and $\mathbf{V}_C$, and the current $\mathbf{I}$.
f. Verify Kirchhoff's voltage law around the closed loop.
g. Find the average power delivered to the circuit.
h. Find the power factor of the circuit, and indicate whether it is leading or lagging.
i. Find the sinusoidal expressions for the voltages and current.
j. Plot the waveforms for the voltages and current on the same set of axes.
(FIGURE CAN'T COPY)

Linda Winkler
Linda Winkler
Numerade Educator

Problem 11

Repeat Problem 10 for the circuit in Fig. 15.130.
(FIGURE CAN'T COPY)

Check back soon!
02:14

Problem 12

Using the oscilloscope reading in Fig. 15.131, determine the resistance $R$.
(FIGURE CAN'T COPY)

Vishal Gupta
Vishal Gupta
Numerade Educator
02:37

Problem 13

Using the DMM current reading and the oscilloscope measurement in Fig. 15.132:
a. Determine the inductance $L$.
b. Find the resistance $R$.
(FIGURE CAN'T COPY)

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:52

Problem 14

Using the oscilloscope reading in Fig. 15.133, determine the capacitance $C$.
(FIGURE CAN'T COPY)

Artemisa Mazón
Artemisa Mazón
Numerade Educator
02:56

Problem 15

Calculate the voltages $\mathbf{V}_1$ and $\mathbf{V}_2$ for the circuits in Fig. 15.134 in phasor form using the voltage divider rule.
(FIGURE CAN'T COPY)

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:56

Problem 16

Calculate the voltages $\mathbf{V}_1$ and $\mathbf{V}_2$ for the circuits in Fig. 15.135 in phasor form using the voltage divider rule.
(FIGURE CAN'T COPY)

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator

Problem 17

For the circuit in Fig. 15.136:
a. Determine $\mathbf{I}, \mathbf{V}_R$, and $\mathbf{V}_C$ in phasor form.
b. Calculate the total power factor, and indicate whether it is leading or lagging.
c. Calculate the average power delivered to the circuit.
d. Draw the impedance diagram.
e. Draw the phasor diagram of the voltages $\mathbf{E}, \mathbf{V}_R$, and $\mathbf{V}_C$. and the current $\mathbf{I}$.
f. Find the voltages $\mathbf{V}_R$ and $\mathbf{V}_C$ using the voltage divider rule, and compare them with the results of part (a) above.
g. Draw the equivalent series circuit of the above as far as the total impedance and the current $i$ are concerned.
(FIGURE CAN'T COPY)

Check back soon!
01:20

Problem 18

Repeat Problem 17 if the capacitance is changed to $220 \mu \mathrm{F}$.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:19

Problem 19

An electrical load has a power factor of 0.8 lagging. It dissipates $8 \mathrm{~kW}$ at a voltage of $200 \mathrm{~V}$. Calculate the impedance of this load in rectangular coordinates.

Narayan Hari
Narayan Hari
Numerade Educator
02:40

Problem 20

Find the series element or elements that must be in the enclosed container in Fig. 15.137 to satisfy the following conditions:
a. Average power to circuit $=300 \mathrm{~W}$.
b. Circuit has a lagging power factor.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 21

For the circuit in Fig. 15.138:
a. Plot $Z_T$ and $\theta_T$ versus frequency for a frequency range of zero to $20 \mathrm{kHz}$.
b. Plot $V_L$ versus frequency for the frequency range of part (a).
c. Plot $\theta_L$ versus frequency for the frequency range of part (a).
d. Plot $V_R$ versus frequency for the frequency range of part (a).

Check back soon!

Problem 22

For the circuit in Fig. 15.139:
a. Plot $Z_T$ and $\theta_T$ versus frequency for a frequency range of zero to $10 \mathrm{kHz}$.
b. Plot $V_C$ versus frequency for the frequency range of part (a).
c. Plot $\theta_C$ versus frequency for the frequency range of part (a).
d. Plot $V_R$ versus frequency for the frequency range of part (a).

Check back soon!

Problem 23

For the series $R$-L-C circuit in Fig. 15.140:
a. Plot $Z_T$ and $\theta_T$ versus frequency for a frequency range of zero to $20 \mathrm{kHz}$ in increments of $1 \mathrm{kHz}$.
b. Plot $V_C$ (magnitude only) versus frequency for the same frequency range of part (a).
c. Plot $I$ (magnitude only) versus frequency for the same frequency range of part (a).

Check back soon!
View

Problem 24

For the series $R$-C circuit in Fig. 15.141:
a. Determine the frequency at which $X_C=R$.
b. Develop a mental image of the change in total impedance with frequency without resorting to a single calculation.
c. Find the total impedance at $100 \mathrm{~Hz}$ and $10 \mathrm{kHz}$, and compare your answer with the assumptions of part (b).
d. Plot the curve of $\mathbf{V}_C$ versus frequency.
e. Find the phase angle of the total impedance at $f=40 \mathrm{kHz}$. Is the network resistive or capacitive at this frequency?

Lainey Roebuck
Lainey Roebuck
Numerade Educator

Problem 25

Find the total admittance and impedance of the circuits in Fig. 15.142. Identify the values of conductance and susceptance, and draw the admittance diagram.

Check back soon!

Problem 26

Find the total admittance and impedance of the circuits in Fig. 15.143. Identify the values of conductance and susceptance, and draw the admittance diagram.

Check back soon!
04:07

Problem 27

Repeat Problem 6 for the parallel circuit elements that must be in the closed container for the same voltage and current to exist at the input terminals. (Find the simplest parallel circuit that will satisfy the conditions indicated.)

Sheh Lit Chang
Sheh Lit Chang
University of Washington

Problem 28

For the circuit in Fig. 15.144:
a. Find the total admittance $\mathbf{Y}_T$ in polar form.
b. Draw the admittance diagram.
c. Find the voltage $\mathbf{E}$ and the currents $\mathbf{I}_R$ and $\mathbf{I}_L$ in phasor form.
d. Draw the phasor diagram of the currents $\mathbf{I}_x, \mathbf{I}_R$, and $\mathbf{I}_L$, and the voltage $\mathbf{E}$.
e. Verify Kirchhoff's current law at one node.
f. Find the average power delivered to the circuit.
g. Find the power factor of the circuit, and indicate whether it is leading or lagging.
h. Find the sinusoidal expressions for the currents and voltage if the frequency is $60 \mathrm{~Hz}$.
i. Plot the waveforms for the currents and voltage on the same set of axes.

Check back soon!

Problem 29

Repeat Problem 28 for the circuit in Fig. 15.145, replacing $\mathbf{I}_L$ with $\mathbf{I}_C$ in parts (c) and (d).
(FIGURE CAN'T COPY)

Check back soon!

Problem 30

Repeat Problem 28 for the circuit in Fig. 15.146, replacing $\mathbf{E}$ with $\mathbf{I}_{\mathrm{s}}$ in part (c).
(FIGURE CAN'T COPY)

Check back soon!

Problem 31

For the circuit in Fig. 15.147:
a. Find the total admittance and impedance in polar form.
b. Draw the admittance and impedance diagrams.
c. Find the value of $C$ in microfarads and $L$ in henries.
d. Find the voltage $\mathbf{E}$ and currents $\mathbf{I}_R, \mathbf{I}_L$, and $\mathbf{I}_C$ in phasor form.
e. Draw the phasor diagram of the currents $\mathbf{I}_R, \mathbf{I}_R, \mathbf{I}_L$, and $\mathbf{I}_c$, and the voltage $\mathbf{E}$.
f. Verify Kirchhoff's current law at one node.
g. Find the average power delivered to the circuit.
h. Find the power factor of the circuit, and indicate whether it is leading or lagging.
i. Find the sinusoidal expressions for the currents and voltage.
j. Plot the waveforms for the currents and voltage on the same set of axes.
(FIGURE CAN'T COPY)

Check back soon!

Problem 32

Repeat Problem 31 for the circuit in Fig. 15.148.
(FIGURE CAN'T COPY)

Check back soon!

Problem 33

Repeat Problem 31 for the circuit in Fig. 15.149, replacing $e$ with $i_x$ in part (d).
(FIGURE CAN'T COPY)

Check back soon!

Problem 34

Calculate the currents $\mathbf{I}_1$ and $\mathbf{I}_2$ in Fig. 15.150 in phasor form using the current divider rule.
(FIGURE CAN'T COPY)

Check back soon!

Problem 35

For the parallel $R$ - $C$ network in Fig. 15.151:
a. Plot $Z_T$ and $\theta_T$ versus frequency for a frequency range of zero to $20 \mathrm{kHz}$.
b. Plot $V_C$ versus frequency for the frequency range of part (a).
c. Plot $I_R$ versus frequency for the frequency range of part (a).
(FIGURE CAN'T COPY)

Check back soon!

Problem 36

For the parallel $R-L$ network in Fig. 15.152:
a. Plot $Z_T$ and $\theta_T$ versus frequency for a frequency range of zero to $10 \mathrm{kHz}$.
b. Plot $I_L$ versus frequency for the frequency range of part (a).
c. Plot $I_R$ versus frequency for the frequency range of part (a).
(FIGURE CAN'T COPY)

Check back soon!

Problem 37

Plot $Y_T$ and $\theta_T$ (of $\mathbf{Y}_T=Y_T \angle \theta_T$ ) for a frequency range of zero to $20 \mathrm{kHz}$ for the network in Fig. 15.151.

Check back soon!

Problem 38

Plot $Y_T$ and $\theta_T$ (of $\mathbf{Y}_T=Y_T \angle \theta_T$ ) for a frequency range of zero to $10 \mathrm{kHz}$ for the network in Fig. 15.152.

Check back soon!

Problem 39

For the parallel $R$ - $L$-C network in Fig. 15.153:
a. Plot $Y_T$ and $\theta_T$ (of $\mathbf{Y}_T=Y_T \angle \theta_T$ ) for a frequency range of zero to $20 \mathrm{kHz}$.
b. Repeat part (a) for $Z_T$ and $\theta_T$ (of $\mathbf{Z}_T=Z_T \angle \theta_T$ ).
c. Plot $V_C$ versus frequency for the frequency range of part (a).
d. Plot $I_L$ versus frequency for the frequency range of part (a).

Check back soon!
01:32

Problem 40

For the series circuits in Fig. 15.154, find a parallel circuit that will have the same total impedance $\left(\mathbf{Z}_T\right)$.
(FIGURE CAN'T COPY)

Aman Gupta
Aman Gupta
Numerade Educator

Problem 41

For the parallel circuits in Fig. 15.155, find a series circuit that will have the same total impedance.
(FIGURE CAN'T COPY)

Check back soon!
01:00

Problem 42

For the network in Fig. 15.156:
a. Calculate $\mathbf{E}, \mathbf{I}_R$. and $\mathbf{I}_L$ in phasor form.
b. Calculate the total power factor, and indicate whether it is leading or lagging.
c. Calculate the average power delivered to the circuit.
d. Draw the admittance diagram.
e. Draw the phasor diagram of the currents $\mathbf{I}_s, \mathbf{I}_R$, and $\mathbf{I}_L$. and the voltage $\mathbf{E}$.
f. Find the current $\mathbf{I}_C$ for each capacitor using only Kirchhoff's current law.
g. Find the series circuit of one resistive and reactive element that will have the same impedance as the original circuit.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator

Problem 43

Repeat Problem 42 if the inductance is changed to $1 \mathrm{H}$.

Check back soon!

Problem 44

Find the element or elements that must be in the closed container in Fig. 15.157 to satisfy the following conditions. (Find the simplest parallel circuit that will satisfy the indicated conditions.)
a. Average power to the circuit $=3000 \mathrm{~W}$.
b. Circuit has a lagging power factor.
(FIGURE CAN'T COPY)

Check back soon!

Problem 45

For the circuit in Fig. 15.158, determine the phase relationship between the following using a dual-trace oscilloscope. The circuit can be reconstructed differently for each part, bu do not use sensing resistors. Show all connections on a redrawn diagram.
a. $e$ and $v_C$
b. $e$ and $i_s$
c. $e$ and $v_L$
(FIGURE CAN'T COPY)

Check back soon!

Problem 46

For the network in Fig. 15.159, determine the phase relationship between the following using a dual-trace oscilloscope. The network must remain as constructed in Fig. 15.159, but sensing resistors can be introduced. Show all connections on a redrawn diagram.
a. $e$ and $v_{R_1}$
b. $e$ and $i_s$
c. $i_L$ and $i_C$

Check back soon!

Problem 47

For the oscilloscope traces in Fig. 15.160:
a. Determine the phase relationship between the waveforms, and indicate which one leads or lags.
b. Determine the peak-to-peak and rms values of each waveform.
c. Find the frequency of each waveform.

Check back soon!
10:35

Problem 48

For the network in Fig. 15.126 (use $f=1 \mathrm{kHz}$ ):
a. Determine the rms values of the voltages $\mathbf{V}_R$ and $\mathbf{V}_L$ and the current $\mathbf{I}$.
b. Plot $v_R, v_L$, and $i$ versus time on separate plots.
c. Place $e, v_R, v_L$, and $i$ on the same plot, and label accordingly.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator

Problem 49

For the network in Fig. 15.146:
a. Determine the rms values of the currents $\mathbf{I}_s, \mathbf{I}_R$, and $\mathbf{I}_L$.
b. Plot $i_S, i_R$, and $i_L$ versus time on separate plots.
c. Place $e, i_s, i_R$, and $i_L$ on the same plot, and label accordingly.

Check back soon!

Problem 50

For the network in Fig. 15.128:
a. Plot the impedance of the network versus frequency from 0 to $10 \mathrm{kHz}$.
b. Plot the current $i$ versus frequency for the frequency range zero to $10 \mathrm{kHz}$.

Check back soon!

Problem 51

For the network in Fig. 15.136:
a. Find the $\mathrm{rms}$ values of the voltages $v_R$ and $v_C$ at a frequency of $1 \mathrm{kHz}$.
b. Plot $v_C$ versus frequency for the frequency range zero to $10 \mathrm{kHz}$.
c. Plot the phase angle between $e$ and $i$ for the frequency range zero to $10 \mathrm{kHz}$.

Check back soon!