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Principles and Applications of Electrical Engineering

Giorgio Rizzoni

Chapter 7

AC Power - all with Video Answers

Educators

Chapter Questions

00:42

Problem 1

The heating element in a soldering iron has a resistance of $391 \Omega$. Find the average power dissipated in the soldering iron if it is connected to a voltage source of 117 V rms.

Netra Sharma
Netra Sharma
University of Wisconsin - Milwaukee
01:45

Problem 2

The heating element in an electric heater has a resistance of $10 \Omega$. Find the power dissipated in the heater when it is connected to a voltage source of $240 \mathrm{~V} \mathrm{ms}$.

00000 00000
00000 00000
Numerade Educator
07:57

Problem 3

A current source $i(t)$ is connected to a $100-\Omega$ resistor. Find the average power delivered to the resistor, given that $i(t)$ is:
a. $4 \cos 100 t \mathrm{~A}$
b. $4 \cos (100 t-0.873) \mathrm{A}$
c. $4 \cos 100 t-3 \cos (100 t-0.873) \mathrm{A}$
d. $4 \cos 100 t-3 \mathrm{~A}$

Vishal Gupta
Vishal Gupta
Numerade Educator

Problem 4

Find the rms value of each of the following periodic currents:
a. $\cos 377 t+\cos 377 t$
b. $\cos 2 t+\sin 2 t$
c. $\cos 377 t+1$
d. $\cos 2 t+\cos (2 t+3 \pi / 4)$
e. $\cos 2 t+\cos 3 t$

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07:34

Problem 5

A current of 10 A rms flows when a single-phase circuit is placed across a $220-\mathrm{V}$ rms source. The current lags the voltage by $\pi / 3$ rad. Find the power dissipated by the circuit and the power factor.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:17

Problem 6

A single-phase circuit is placed across a $120-\mathrm{V}$ rms, $60-\mathrm{Hz}$ source, with an ammeter, a voltmeter, and a wattmeter connected. The instruments indicate 12 A , 120 V , and 800 W , respectively. Find
a. The power factor.
b. The phase angle.
c. The impedance.
d. The resistance.

Salamat Ali
Salamat Ali
Numerade Educator
01:03

Problem 7

The nameplate on a single-phase induction machine reads 2 horsepower (output), $110 \mathrm{~V} \mathrm{mms}, 60 \mathrm{~Hz}$, and 24 A rms. Find the power factor of the machine if the efficiency at rated output is 80 percent. [Note: 1 horsepower $=0.746 \mathrm{~kW}$.]

Narayan Hari
Narayan Hari
Numerade Educator
01:24

Problem 8

Given the waveform of a voltage source shown in Figure P7.8, find:
a. the average and rms values of the voltage.
b. the average power supplied to a $10-\Omega$ resistor connected across the voltage source.

Anurag Kumar
Anurag Kumar
Numerade Educator

Problem 9

For the following numerical values, determine the average power, $P$, the reactive power, $Q$, and the complex power, $S$, of the circuit shown in Figure P7.9. Note: phasor quantities are rms.
a. $v_s(t)=650 \cos (377 t) \mathrm{V}$

$$
i_L(t)=20 \cos (377 t-0.175) \mathrm{A}
$$

b. $\overline{\mathbf{V}}_5=460 \angle 0 \mathrm{~V}$

$$
\tilde{\mathbf{i}}_L=14.14 \angle-\pi / 4 \mathrm{~A}
$$

c. $\overline{\mathbf{V}}_{\mathrm{S}}=100 \angle 0 \mathrm{~V}$

$$
\tilde{\mathbf{i}}_L=8.6 \angle-1.5 \mathrm{~A}
$$

d. $\overline{\mathbf{V}}_S=208 \angle-\pi / 6 \mathrm{~V}$ $\mathrm{i}_L=2.3 \angle-1.1 \mathrm{~A}$

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Problem 10

For the circuit of Figure P7.9, determine the power factor for the load and state whether it is leading or lagging for the following conditions:
a.

$$
\begin{aligned}
& v_s(t)=540 \cos (\omega t+\pi / 12) \mathrm{V} \\
& i_{\mathrm{L}}(t)=20 \cos (\omega t+0.82) \mathrm{A}
\end{aligned}
$$

b.

$$
\begin{aligned}
& v_s(t)=155 \cos (\omega t-\pi / 12) \mathrm{V} \\
& i_{\mathrm{I}}(t)=20 \cos (\omega t-0.384) A
\end{aligned}
$$

c.

$$
\begin{aligned}
& \operatorname{vs}_s(t)=208 \cos (\omega t) \mathrm{V} \\
& i_{\mathrm{L}}(t)=1.7 \sin (\omega t+3.054) \mathrm{A}
\end{aligned}
$$

d. $Z_L=(48+j 16) \Omega$

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Problem 11

For the circuit of Figure P7.9, determine whether the load is capacitive or inductive for the circuit shown if
a. $\mathrm{pf}=0.87$ (leading)
b. $\mathrm{pf}=0.42$ (leading)
c.

$$
\begin{aligned}
& v_S(t)=42 \cos (\omega t) \\
& i_{\mathrm{L}}(t)=4.2 \sin (\omega t) \\
& v_S(t)=10.4 \cos (\omega t-\pi / 15) \\
& i_{\mathrm{L}}(t)=0.4 \cos (\omega t-\pi / 15)
\end{aligned}
$$

d.

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04:11

Problem 12

Find the real and reactive power supplied by the source in the circuit shown in Figure P7.12.

Narayan Hari
Narayan Hari
Numerade Educator

Problem 13

For the circuit shown in Figure P7.13, find the real and reactive power supplied by each source. The sources are $\overline{\mathbf{V}}_{t 1}=36 \angle-\pi / 3 \mathrm{~V}$ and $\overline{\mathbf{V}}_{t 2}=$ 24 $\angle 0.644 \mathrm{~V}$.

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03:27

Problem 14

The load $Z_L$ in the circuit of Figure P7. 14 consists of a $25-\Omega$ resistor in parallel with a $100-\mu \mathrm{F}$ capacitor. Assume $\omega=377 \mathrm{rad} / \mathrm{s}$. Calculate
a. The apparent power delivered to the load.
b. The apparent power supplied by the source.
c. The power factor of the load.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:11

Problem 15

Calculate the apparent power, real power, and reactive power for the circuit shown in Figure P7.15. Draw the power triangle.

Narayan Hari
Narayan Hari
Numerade Educator
01:48

Problem 16

A single-phase motor draws 220 W at a power factor of 80 percent (lagging) when connected across a $200-\mathrm{V}, 60-\mathrm{Hz}$ source. A capacitor is connected in parallel with the load to give a unity power factor, as shown in Figure P7.16. Find the required capacitance.

Anurag Kumar
Anurag Kumar
Numerade Educator
04:53

Problem 17

Suppose that the electricity in your home has gone out and the power company will not be able to have you hooked up again for several days. The freezer in the basement contains several hundred dollars" worth of food that you cannot afford to let spoil. You have also been experiencing very hot, humid weather and would like to keep one room air-conditioned with a window air conditioner, as well as run the refrigerator in your kitchen. When the appliances are on, they draw the following currents (all values are ms):

$$
\begin{aligned}
\text { Air conditioner: } & 9.6 \mathrm{~A} @ 120 \mathrm{~V} \\
& \mathrm{pf}=0.90 \text { (lagging) } \\
\text { Freener: } & 4.2 \mathrm{~A} @ 120 \mathrm{~V} \\
& \mathrm{pf}=0.87 \text { (lagging) } \\
\text { Refrigerator: } & 3.5 \mathrm{~A} @ 120 \mathrm{~V} \\
& \mathrm{pf}=0.80 \text { (lagging) }
\end{aligned}
$$

In the worst-case scenario, how much power must an emergency generator supply?

Anurag Kumar
Anurag Kumar
Numerade Educator

Problem 18

The load on a single-phase three-wire system in a home is generally not balanced. For the system shown in Figure P7.18, let $\overline{\mathbf{V}}_{\mathrm{s} 1}=115 \angle 0 \mathrm{~V}_{\mathrm{mas}}$ and $\tilde{\mathbf{V}}_{x 2}=115 \angle 0 \mathrm{~V}_{\max }$. Determine:
a. The total average power delivered to the connected loads: $Z_{L 1}, Z_{L 2}$, and $Z_{L 3}$.
b. The total average power lost in the lines: $Z_{g 1}, Z_{f 2}$, and $Z_n$.
c. The average power supplied by each source.

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01:01

Problem 19

A large consumer of electricity requires 10 kW of power at $230 \mathrm{~V}_{\mathrm{max}}$ at a pf angle of $\pi / 3 \mathrm{rad}$ lagging. The transmission line between the electric utility and the consumer has a resistance of $0.1 \Omega$. If the consumer can increase the pf from 0.5 to 0.9 lagging, determine the change in transmission line losses and lood current.

Narayan Hari
Narayan Hari
Numerade Educator
02:30

Problem 20

A $1000-\mathrm{W}$ electric motor is connected to a source of $120 \mathrm{~V}_{\mathrm{mm}}, 60 \mathrm{~Hz}$, and the result is a lagging pf of 0.8 . To correct the pf to 0.95 lagging, a capacitor is placed in parallel with the motor. Calculate the current drawn from the source with and without the capacitor connected. Determine the value of the capacitor required to make the correction.

Anurag Kumar
Anurag Kumar
Numerade Educator

Problem 21

If the voltage and current given below are supplied by a source to a circuit or load, determine:
a. The power supplied by the source which is dissipated as heat or work in the circuit (load).
b. The power stored in reactive components in the circuit (load).
c. The power factor angle and the power factor.

$$
\tilde{\mathbf{V}}_x=7 \angle 0.873 \mathrm{~V} \quad \hat{\mathbf{i}}_x=13 \angle-0.349 \mathrm{~A}
$$

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01:40

Problem 22

Determine $C$ so that the plant power factor of Figure P7.22 is corrected to 1 ; i.e, $\tilde{\mathbf{i}}_{\text {s }}$ is minimized and in phase with $\overline{\mathbf{V}}_o$.

$$
\begin{aligned}
v_x(t) & =450 \cos (\omega t) \mathrm{V} \quad \omega=377 \mathrm{rad} / \mathrm{s} \\
\mathrm{Z} & =7+j 1 \Omega \\
\mathrm{Z}_G & =3+j 0.11 \mathrm{~m} \Omega
\end{aligned}
$$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:40

Problem 23

Determine $C$ so that the plant power factor of Figure P7. 22 is corrected to 1 (or the power factor angle to zero) so that $\overrightarrow{\mathbf{i}}_s$ is minimined and in phase with $\overline{\mathbf{V}}_{\text {}}$.

$$
\begin{aligned}
v_x(t) & =450 \cos (\omega t) \mathrm{V} \quad \omega t=377 \mathrm{rad} / \mathrm{s} \\
Z & =7 \angle 0.175 \Omega
\end{aligned}
$$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:26

Problem 24

Without the capacitor connected into the circuit of Figure P7.22,

$$
\begin{array}{rlrl}
\overline{\mathbf{V}}_e & =450 \angle 0 \mathrm{~V} & & \tilde{\mathbf{i}}_{\mathrm{a}} \\
= & =17 \angle-0.175 \mathrm{~A} \\
f & =60 \mathrm{~Hz} & & C=17.40 \mu \mathrm{~F}
\end{array}
$$

The value of $C$ is that which will correct the power factor angle to zero, i.e., reduces $\overrightarrow{\mathbf{i}}_8$ to a minimum value in phase with $\tilde{\mathbf{V}}_a$. Determine the reduction of current which resulted from connecting the capacitor into the circuit.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
05:22

Problem 25

Without the capacitor connected into the circuit:

$$
\begin{aligned}
v_\mu(t) & =170 \cos \omega t \mathrm{~V} \\
i_n(t) & =130 \cos (\omega t-0.192) \mathrm{A} \\
f & =60 \mathrm{~Hz} \quad C=387 \mu \mathrm{~F}
\end{aligned}
$$

The value of $C$ given is that which will correct the power factor angle to zero, i.e., reduces $\overrightarrow{\mathbf{i}}_i$ to a minimum value in phase with $\overline{\mathbf{V}}_2$. Determine by how much the current supplied to the plant is reduced by connecting the capacitor.

Keshav Singh
Keshav Singh
Numerade Educator

Problem 26

Determine the time-averaged total power, the real power dissipated, and the reactive power stored in each of the impedances in the circuit shown in Figure P7. 26 if

$$
\begin{aligned}
\overline{\mathbf{V}}_{\mathrm{s1}} & =170 \angle 0 \mathrm{~V} \\
\overline{\mathbf{V}}_{n 2} & =170 \mathrm{~V} \angle(\pi / 2) \mathrm{V} \\
& =377 \mathrm{rad} / \mathrm{s} \\
\mathrm{Z}_1 & =0.7 \angle(\pi / 6) \Omega \\
\mathrm{Z}_2 & =1.5 \angle 0.105 \Omega \\
\mathrm{Z}_3 & =0.3+j 0.4 \Omega
\end{aligned}
$$

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Problem 27

If the voltage and current supplied to a circuit of load by a source are:

$$
\overline{\mathbf{V}}_{\mathrm{A}}=170 \angle-0.157^2 \mathrm{~V} \quad \overline{\mathbf{i}}_{\mathrm{s}}=13 \angle 0.28^2 \mathrm{~A}
$$

Determine:
a. The power supplied by the source which is dissipated as heat or work in the circuit (load).
b. The power stored in reactive components in the circuit (load).
c. The power factor angle and power factor.
ection 3: Transformers

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06:02

Problem 28

A center-tap transformer has the schematic representation shown in Figure P7.28. The primary-side voltage is stepped down to a secondary-side voltage, $\overline{\mathbf{v}}_{\mathrm{mc}}$, by a ratio of $n: 1$. On the secondary side, $\overline{\mathbf{V}}_{\text {sct }}=\overline{\mathbf{V}}_{\mathrm{mc2}}=\frac{1}{\mathrm{i}} \overline{\mathbf{v}}_{\mathrm{mc}}$.
a. If $\dot{\mathbf{V}}_{\mathrm{pin}}=120 \angle 32^{\circ} \mathrm{V}$ and $n=9$, find $\tilde{\mathbf{V}}_{\mathrm{mac}}, \tilde{\mathbf{V}}_{\mathrm{macl}}$, and $\dot{\mathbf{V}}_{\mathrm{mcI}}$.
b. What must $n$ be if $\overline{\mathbf{V}}_{\text {peim }}=208 \angle 0.175 \mathrm{~V}$ and we desire $\left|\tilde{\mathbf{V}}_{\mathrm{mac}}\right|$ to be 8.7 V ?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator

Problem 29

For the circuit shown in Figure P7.29, find:
a. The total resistance seen by the voltage source.
b. The voltage gain $v_2 / v_k$.
c. The value to which the $16-\Omega$ load resistance should be changed so it will absorb maximum power from the given source.

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02:25

Problem 30

An ideal transformer is rated to deliver 400 kVA at 460 V to a customer as shown in Figure P7. 30.
a. How much current can the transformer supply to the customer?
b. If the customer's load is purely resistive (i.e., if $\mathrm{pf}=1$ ), what is the maximum power that the customer can receive?
c. If the customer's power factor is 0.8 (lagging), what is the maximum usable power the customer can receive?
d. What is the maximum power if the pf is 0.7 (lagging)?
e. If the customer requires 300 kW to operate, what is the minimum power factor with the given size transformer?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:14

Problem 31

For the ideal transformer shown in Figure P7.31, find $v_a(t)$ if $v_s(t)$ is $294 \cos 377 t$.

Kajal Gautam
Kajal Gautam
Numerade Educator
01:53

Problem 32

If the transformer shown in Figure P7.32 is ideal, find the turns ratio $N=1 / n$ that will provide maximum power transfer to the load.

Kajal Gautam
Kajal Gautam
Numerade Educator
02:34

Problem 33

Assume the $8-\Omega$ resistor is the load in the circuit shown in Figure P7.33. Assume a turns ratio of $1: n$, What value of $n$ will result in the load resistor absorbing maximum power from the source?

Kajal Gautam
Kajal Gautam
Numerade Educator
08:04

Problem 34

If we knew that the transformer shown in Figure P7.34 was to deliver 50 A at 110 V rms with a certain resistive load, what rms phasor voltage source, $\mathbf{V}_5$, would provide this voltage and current?

M Hassan Anwar
M Hassan Anwar
Numerade Educator

Problem 35

A method for determining the equivalent circuit of a transformer consists of two tests: the open-circuit test and the short-circuit test. The open-circuit test, shown in Figure P7.35(a), is usually done by applying rated voltage to the primary side of the transformer while leaving the secondary side open. The current into the primary side is measured, as is the power dissipated.
FIGURE CAN'T COPY.

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Problem 36

Using the methods of Problem 7.35 and the following data, find the equivalent circuit of the transformer tested:

Open-circuit test:

$$
\begin{aligned}
& \overline{\mathbf{V}}_P=4,600 \mathrm{~V} \\
& \overline{\mathbf{i}}_{\mathrm{OC}}=0.7 \mathrm{~A} \\
& P=200 \mathrm{~W} \\
& P=50 \mathrm{~W} \\
& \overline{\mathbf{V}}_P=5.2 \mathrm{~V}
\end{aligned}
$$

The transformer is a $460-\mathrm{kVA}$ transformer, and the tests are performed at 60 Hz
ection 4: Three-Phase Power

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01:50

Problem 37

The magnitude of the phase voltage of a balanced three-phase wye system is 100 V . Express each phase and line voltage in both polar and rectangular coordinates.

Narayan Hari
Narayan Hari
Numerade Educator
02:25

Problem 38

The phase currents in a four-wire wye-connected lood are as follows:

$$
\tilde{\mathbf{i}}_{\mathrm{ca}}=10 \angle 0, \tilde{\mathbf{i}}_{\mathrm{ic}}=12 \angle 5 \pi / 6, \tilde{\mathbf{i}}_{c \mathrm{~s}}=8 \angle 2.88
$$

Determine the current in the neutral wire.

Kajal Gautam
Kajal Gautam
Numerade Educator

Problem 39

For the circuit shown in Figure P7.39, we see that each voltage source has a phase difference of $2 \pi / 3$ in relation to the others.
a. Find $\overline{\mathbf{V}}_{E W}, \overline{\mathbf{V}}_{W E}$, and $\overline{\mathbf{V}}_{E R}$, where

$$
\begin{aligned}
& \overline{\mathbf{V}}_{\mathrm{F} W}=\tilde{\mathbf{V}}_{\mathrm{R}}-\tilde{\mathbf{V}}_{\mathrm{W}}, \overline{\mathbf{V}}_{\mathrm{WI}}=\overline{\mathbf{V}}_{\mathrm{W}}-\overline{\mathbf{V}}_{\mathrm{B}}, \text { and } \\
& \overline{\mathbf{V}}_{n R}=\overline{\mathbf{V}}_n-\hat{\mathbf{v}}_n \text {. }
\end{aligned}
$$

b. Repeat part a, using the calculations

$$
\begin{aligned}
& \overline{\mathbf{V}}_{R W}=\overrightarrow{\mathbf{V}}_R \sqrt{3} \angle-\pi / 6 \\
& \mathbf{V}_{W I}=\mathbf{V}_W \sqrt{3} \angle-\pi / 6 \\
& \mathbf{v}_{A R}=\mathrm{V}_{\mathrm{I}} \sqrt{3} \angle-\pi / 6
\end{aligned}
$$

c. Compare the results of part a with the results of part b.

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06:52

Problem 40

For the three-phase circuit shown in Figure P7.40, find the currents $\tilde{\mathbf{I}}_W, \tilde{\mathbf{I}}_g, \tilde{\mathbf{I}}_g$, and $\tilde{\mathbf{I}}_{\mathcal{N}}$.

NT
Nikhil Tiwari
Numerade Educator
14:54

Problem 41

For the circuit shown in Figure P7.41, find the currents $\tilde{\mathbf{i}}_R, \tilde{\mathbf{i}}_W, \tilde{\mathbf{i}}_B$, and $\tilde{\mathbf{i}}_N$.

Brandy Heflin
Brandy Heflin
Numerade Educator

Problem 42

In the circuit of Figure P7.42:

$$
\begin{aligned}
v_{\mathrm{l} 1} & =170 \cos (\omega \mathrm{t}) \mathrm{V} \\
v_{\mathrm{l} 2} & =170 \cos (\omega \mathrm{t}+2 \pi / 3) \mathrm{V} \\
v_{\mathrm{l} 3} & =170 \cos (\omega \mathrm{t}-2 \pi / 3) \mathrm{V} \\
f & =60 \mathrm{~Hz} \quad Z_1=0.5 \angle 20^2 \Omega \\
Z_2 & =0.35 \angle 0^{\circ} \Omega \quad Z_5=1.7 \angle-90^{\circ} \Omega
\end{aligned}
$$
Determine the current through $Z_1$ using:
a. Loop/mesh amalysis.
b. Node analysis.
c. Superposition.

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Problem 43

Determine the current through $R$ in the circuit of Figure P7.43:

$$
\begin{aligned}
\mathrm{v}_1 & =170 \cos (\omega t) \mathrm{V} \\
\mathrm{v}_2 & =170 \cos (\omega t)-2 \pi / 3) \mathrm{V} \\
\mathrm{v}_3 & =170 \cos (\omega t+2 \pi / 3) \mathrm{V} \\
f & =400 \mathrm{~Hz} \quad R=100 \Omega \\
\mathrm{C} & =0.47 \mu \mathrm{~F} \quad L=100 \mathrm{mH}
\end{aligned}
$$

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Problem 44

The three sources in the circuit of Figure P7.44 are connected in wye configuration and the loads in a delta configuration. Determine the current through each impedance.

$$
\begin{aligned}
v_{x 1} & =170 \cos (\omega t) \mathrm{V} \\
v_{x 2} & =170 \cos (\omega t+2 \pi / 3) \mathrm{V} \\
v_{A S} & =170 \cos (\omega t-2 \pi / 3) \mathrm{V} \\
f & =60 \mathrm{~Hz} \quad Z_1=3 \angle 0 \Omega \\
Z_2 & =7 \angle \pi / 2 \Omega \quad Z_3=0-j 11 \Omega
\end{aligned}
$$

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Problem 45

If we model each winding of a three-phase motor like the circuit shown in Figure P7.45(a) and connect the windings as shown in Figure P7.45(b), we have the three-phase circuit shown in Figure P7.45(c). The motor can be constructed so that $R_1=R_2=R_3$ and $L_1=L_2=L_3$, as is the usual case. If we connect the motor as shown in Figure P7.45(c), find the currents $\tilde{\mathbf{i}}_n, \tilde{\mathbf{i}}_w, \tilde{\mathbf{i}}_s$, and $\mathbf{i}_N$, assuming that the resistances are $40 \Omega$ each and each inductance is 5 mH . The frequency of each of the sources is 60 Hz .

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03:17

Problem 46

With reference to the motor of Problem 7.44,
a. How much power (in watts) is delivered to the motor?
b. What is the motor's power factor?
c. Why is it common in industrial practice not to connect the ground lead to motors of this type?

Salamat Ali
Salamat Ali
Numerade Educator
06:27

Problem 47

Find the apparent power and the real power delivered to the load in the $\mathrm{Y}-\Delta$ circuit shown in Figure P7.47. What is the power factor? Assume rms values.

Kajal Gautam
Kajal Gautam
Numerade Educator

Problem 48

The electric power company is concerned with the loading of its transformers. Since it is responsible to a large number of customers, it must be certain that it can supply the demands of all customers. The power company's transformers will deliver rated kVA to the secondary load. However, if the demand were to increase to a point where greater than rated current were required, the secondary voltage would have to drop below rated value. Also, the current would increase, and with it the $I^2 R$ losses (due to winding resistance), possibly causing the transformer to overheat. Unreasonable current demand could be caused, for example, by excessively low power factors at the load.

The customer, on the other hand, is not greatly concerned with an inefficient power factor, provided that sufficient power reaches the lood. To make the customer more aware of power factor considerations, the power company may install a penalty on the customer's bill. A typical penalty-power factor chart is shown in Table 7.3. Power factors below 0.7 are not permitted. A 25 percent penalty will be applied to any billing after two consecutive months in which the customer's power factor has remained below 0.7 .
TABLE CAN'T COPY.
The $\mathrm{Y}=\mathrm{Y}$ circuit shown in Figure P7.48 is representative of a three-phase motor load. Assume m ms values.
a. Find the total power supplied to the motor.
b. Find the power converted to mechanical energy if the motor is 80 percent efficient.
c. Find the power factor.
d. Does the company risk facing a povaer factor penalty on its next bill if all the motors in the factory are similar to this one?

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02:23

Problem 49

A balanced, three-phase Y-connected source with $230-\mathrm{V}_{\mathrm{mm}}$ line voltages has a balanced Y -connected load of $3+j 4 \Omega$ per phase. For the case that the lines have zero impedance, find all three line currents and the total real power ahsorbed by the load.

Narayan Hari
Narayan Hari
Numerade Educator
04:00

Problem 50

The circuit shown in Figure P7. 50 is a $\mathrm{Y}-\Delta$-Y connected three-phase circuit. The primaries of the transformers are wye-connected, the secondaries are delta-connected, and the load is wye-connected. Find the currents $\overline{\mathbf{I}}_{n F}, \overline{\mathbf{i}}_{W F}, \overline{\mathbf{i}}_{B F}, \overline{\mathbf{i}}_A, \overline{\mathbf{i}}_B$, and $\overline{\mathbf{i}}_C$.

Kajal Gautam
Kajal Gautam
Numerade Educator
04:32

Problem 51

For the circuit shown in Figure P7.51, find the currents $\overrightarrow{\boldsymbol{I}}_A, \vec{I}_B, \hat{\boldsymbol{I}}_C$, and $\boldsymbol{I}_N$, and the real power dissipated by the load.

Thomas Thompson
Thomas Thompson
Numerade Educator