Electrical Circuits and Modified MasteringEngineering - With Access
Electrical Circuits and Modified MasteringEngineering - With Access
10th Edition
ISBN: 9780133992793
Author: NILSSON
Publisher: PEARSON
Question
Book Icon
Chapter 3, Problem 1P

(a)

To determine

Show that the given circuit satisfies Kirchhoff’s current law at junction terminals x-y.

(a)

Expert Solution
Check Mark

Answer to Problem 1P

Yes, the given circuit satisfies Kirchhoff’s current law at junction terminals x-y.

Explanation of Solution

Given data:

Refer to Figure given in the textbook.

The voltage delivered by the source is 120V.

PSPICE Simulation:

Draw the circuit diagram in PSpice as shown in Figure 1.

Electrical Circuits and Modified MasteringEngineering - With Access, Chapter 3, Problem 1P , additional homework tip  1

Save the circuit and provide the Simulation Settings as shown in Figure 2.

Electrical Circuits and Modified MasteringEngineering - With Access, Chapter 3, Problem 1P , additional homework tip  2

Now run the simulation and the results will be displayed as shown in Figure 3 by enabling the “Enable Bias Current Display” icon.

Electrical Circuits and Modified MasteringEngineering - With Access, Chapter 3, Problem 1P , additional homework tip  3

From Figure 3, source current is=12A and the node currents i1=4A and i2=8A.

Kirchhoff’s current law states that the current entering the node is equal to the current leaving the node.

In Figure 3, apply Kirchhoff current law at node b. Therefore,

is+i1+i2=0 (1)

Rearrange the equation (1) as follows,

is=i1+i2 (2)

Substitute 12A for is, 4A for i1 and 8A for i2 in equation (2).

12A=4A+8A12A=12A12A12A=0

Hence, the given circuit satisfies Kirchhoff’s current law at junction terminals x-y.

Conclusion:

Thus, yes, the given circuit satisfies Kirchhoff’s current law at junction terminals x-y.

(b)

To determine

Show that the given circuit satisfies Kirchhoff’s voltage law.

(b)

Expert Solution
Check Mark

Answer to Problem 1P

Yes, the given circuit satisfies Kirchhoff’s voltage law.

Explanation of Solution

Given data:

Refer to Figure given in the textbook.

Voltage delivered by the source is 120V.

PSPICE Simulation:

Draw the circuit diagram in PSpice as shown in Figure 4.

Electrical Circuits and Modified MasteringEngineering - With Access, Chapter 3, Problem 1P , additional homework tip  4

Save the circuit and provide the Simulation Settings as shown in Figure 5.

Electrical Circuits and Modified MasteringEngineering - With Access, Chapter 3, Problem 1P , additional homework tip  5

Now run the simulation and the results will be displayed as shown in Figure 3 by enabling the “Enable Bias Current Display” icon and “Enable Bias Voltage Display” icon.

Electrical Circuits and Modified MasteringEngineering - With Access, Chapter 3, Problem 1P , additional homework tip  6

From Figure 6, the voltage v1 across the 4Ω resistor is,

v1=4Ω×12A=48V{1V=1Ω×1A}

The voltage v2 across the 18Ω resistor is,

v2=18Ω×4A=72V{1V=1Ω×1A}

The voltage v3 across the 3Ω resistor is,

v3=3Ω×8A=24V{1V=1Ω×1A}

The voltage v4 across the 6Ω resistor is,

v4=6Ω×8A=48V{1V=1Ω×1A}

Kirchhoff’s voltage law states that the sum of the voltage rise around any closed loop must be equal to the sum of voltage drops around that loop.

In Figure 6, apply Kirchhoff’s voltage law to the loop abda.

vs=v1+v2 (3)

From Figure 6, the source voltage vs is 120V.

Substitute 120V for vs, 48V for v1, and 72V for v2 in equation (3). Therefore,

120V=48V+72V120V=120V120V120V=0

In Figure 6, apply Kirchhoff’s voltage law to the loop bcdb.

v2=v3+v4 (4)

Substitute 72V for v2, 24V for v3, and 48V for v4 in equation (4). Therefore,

72V=24V+48V72V=72V72V72V=0

In Figure 6, apply Kirchhoff’s voltage law to the loop abcda.

vs=v1+v3+v4 (5)

Substitute 120V for vs, 48V for v1, 24V for v3, and 48V for v4 in equation (5). Therefore,

120V=48V+24V+48V120V=120V120V120V=0

Hence, the given circuit satisfies Kirchhoff’s voltage law around every closed loop.

Conclusion:

Thus, yes, the given circuit satisfies Kirchhoff’s voltage law.

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Chapter 3 Solutions

Electrical Circuits and Modified MasteringEngineering - With Access

Ch. 3 - For each of the circuits shown in Fig....Ch. 3 - For each of the circuits shown in Fig....Ch. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Find the equivalent resistance Rab each of the...Ch. 3 - Prob. 9PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - In the voltage-divider circuit shown in Fig. P...Ch. 3 - The no-load voltage in the voltage-divider circuit...Ch. 3 - Assume the voltage divider in Fig. P3.14 has been...Ch. 3 - Find the power dissipated in the resistor in the 5...Ch. 3 - For the current-divider circuit in Fig. P3.19...Ch. 3 - Specify the resistors in the current-divider...Ch. 3 - There is often a need to produce more than one...Ch. 3 - Show that the current in the kth branch of the...Ch. 3 - Prob. 23PCh. 3 - Look at the circuit in Fig. P3.1 (d). Use current...Ch. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Attach a 6 V voltage source between the terminals...Ch. 3 - Find the voltage x in the circuit in Fig. P3.28...Ch. 3 - Find υo in the circuit in Fig. P3.31 using voltage...Ch. 3 - Find υ1 and υ2 in the circuit in Fig. P3.30 using...Ch. 3 - Prob. 31PCh. 3 - For the circuit in Fig. P3.29, calculate i1 and i2...Ch. 3 - A d'Arsonval ammeter is shown in Fig....Ch. 3 - A shunt resistor and a 50 mV. 1 mA d’Arsonval...Ch. 3 - A d’Arsonval movement is rated at 2 mA and 200 mV....Ch. 3 - Prob. 36PCh. 3 - A d’Arsonval voltmeter is shown in Fig. P3.37....Ch. 3 - Suppose the d’Arsonval voltmeter described in...Ch. 3 - The ammeter in the circuit in Fig. P3. 39 has a...Ch. 3 - The ammeter described in Problem 3.39 is used to...Ch. 3 - The elements in the circuit in Fig2.24. have the...Ch. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - The voltmeter shown in Fig. P3.42 (a) has a...Ch. 3 - The voltage-divider circuit shown in Fig. P3.44 is...Ch. 3 - Assume in designing the multirange voltmeter shown...Ch. 3 - Prob. 47PCh. 3 - Design a d'Arsonval voltmeter that will have the...Ch. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 51PCh. 3 - Prob. 52PCh. 3 - Find the detector current id in the unbalanced...Ch. 3 - Find the current and power supplied by the 40 V...Ch. 3 - Find the current and power supplied by the 40 V...Ch. 3 - Find the current and power supplied by the 40 V...Ch. 3 - Find the equivalent resistance Rab in the circuit...Ch. 3 - Use a Δ-to-Y transformation to find the voltages...Ch. 3 - Find the resistance seen by the ideal voltage...Ch. 3 - Prob. 61PCh. 3 - Find io and the power dissipated in the 140Ω...Ch. 3 - Prob. 63PCh. 3 - Show that the expressions for Δ conductances as...Ch. 3 - Prob. 65PCh. 3 - Prob. 66PCh. 3 - Prob. 67PCh. 3 - The design equations for the bridged-tee...Ch. 3 - Prob. 69PCh. 3 - Prob. 70PCh. 3 - Prob. 71PCh. 3 - Prob. 72PCh. 3 - Prob. 73PCh. 3 - Prob. 74PCh. 3 - Prob. 75P
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