V = 36 VRefer to the figure at the right.izWhat is the potential of point a withrespect to point b when switch S is open?3 0What is the current through switch SSWhen it is closed?What is the equivalent resistance of thiscombination of resistors when S is closed?

Answered: V = 36 V Refer to the figure at the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

V = 36 V
Refer to the figure at the right.
iz
What is the potential of point a with
respect to point b when switch S is open?
3 0
What is the current through switch S
S
When it is closed?
What is the equivalent resistance of this
combination of resistors when S is closed?

Expert Solution

Step 1

The given circuit diagram is shown below:

Step 2

(a)

The circuit diagram when the switch S is open can be drawn as shown below:

The equivalent resistance if the resistance which are in series on the left-hand side and right-hand side of the circuit is:

$R_{35} = R_{3} + R_{5} R_{35} = 6 + 3 R_{35} = 9 Ω$

Similarly,

$R_{26} = R_{2} + R_{6} R_{26} = 3 + 6 R_{26} = 9 Ω$

Thus, these equivalent resistances will be in parallel combination. Therefore, the equivalent resistance of the complete circuit is:

$\frac{1}{R_{e q}} = \frac{1}{R_{35}} + \frac{1}{R_{26}} \frac{1}{R_{e q}} = \frac{1}{9} + \frac{1}{9} R_{e q} = 4.5 Ω$

Step 3

From ohm's law:

$i_{1} = \frac{∆ V}{R_{e q}} i_{1} = \frac{36 - 0}{4.5} i_{1} = 8 A$

Since the resistance on the left-hand side of the circuit is the same as the resistance on the right-hand side of the circuit. Thus, the current flowing through them will be the same:

$i_{2} + i_{3} = i_{1} Therefore, i_{2} = i_{3} i_{3} = \frac{i_{1}}{2} i_{3} = \frac{8}{2} i_{3} = 4 A so, i_{2} = i_{3} = 4 A$

Thus, the potential at point 'a' can be calculated as:

$V_{a} = 36 - i_{3} \times 6 V_{a} = 36 - 4 \times 6 V_{a} = 12 V$

And, the potential at point 'a' can be calculated as:

$V_{b} = 36 - i_{2} \times 3 V_{b} = 36 - 4 \times 3 V_{b} = 24 V$

Therefore, the required potential is:

$V_{a b} = V_{b} - V_{a} V_{a b} = 24 - 12 V_{a b} = 12 V (Ans)$

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