Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 18, Problem 52P

(a)

To determine

Find the equivalent resistance between point A and B.

(a)

Expert Solution
Check Mark

Answer to Problem 52P

The equivalent resistance between point A and B is 3.0 Ω.

Explanation of Solution

The sum of individual resistance connected in series and reciprocal of resistance connected in parallel will give the equivalent resistance.

From the given circuit, consider left 1.0 Ω as R1, 2.0 Ω as R2, top right 1.0 Ω as R3, 4.0 Ω as R4, 8.0 Ω as R5, and 3.3 Ω as R6.

The resistor R4 and R5 are in parallel then the equivalent resistance is,

1R'=1R4+1R5R'=[1R4+1R5]1

This resistance is in series with R6 , then the equivalent resistance is,

R''=R6+R'

The resistance R2 and R3 are in series then the equivalent resistance is,

R'''=R2+R3

The equivalent resistance R'' and R'''  are in parallel then the equivalent resistance is,

1R''''=1R'''+1R''R''''=11R'''+1R''

This resistance is in series with R1 , then the final equivalent resistance is,

Req=R1+R''''

Substitute the values of R' , R'' , R'''  and R'''' in the above equation.

Req=R1+11R2+R3+1R6+[1R4+1R5]1

Conclusion:

Substitute 1.0 Ω for R1, 2.0 Ω for R2, 1.0 Ω for R3, 4.0 Ω for R4, 8.0 Ω for R5, and 3.3 Ω for R6 in the above equation.

Req=1.0 Ω+112.0 Ω+1.0 Ω+13.3 Ω+(14.0 Ω+18.0 Ω)1=1.0 Ω+112.0 Ω+1.0 Ω+13.3 Ω+2.67 Ω=1.0 Ω+113.0 Ω+15.97 Ω=1.0 Ω+1.996 Ω=3.0 Ω

Therefore, the equivalent resistance between point A and B is 3.0 Ω.

(b)

To determine

Find the current through the resistor of resistance 1.0 Ω directly connected to point A.

(b)

Expert Solution
Check Mark

Answer to Problem 52P

The current through the resistor of resistance 1.0 Ω directly connected to point A is 6.0A.

Explanation of Solution

Write the equation for current from emf.

I=εReq (I)

Here, I is current, ε is emf and Req is the equivalent resistance.

Conclusion:

Substitute 18 V for ε and 3.0 Ω for Req in equation I.

I=18 V3.0 Ω=6.0 A

Therefore, the current through the resistor of resistance 1.0 Ω directly connected to point A is 6.0A.

(c)

To determine

Find the current through the resistor of resistance 8.0 Ω.

(c)

Expert Solution
Check Mark

Answer to Problem 52P

The current through the resistor of resistance 8.0 Ω is 0.67A .

Explanation of Solution

The potential difference across the equivalent resistance 1.996 Ω for the large rectangle is 6.0 A×1.996 Ω=11.99V . The current through the bottom of large rectangle of equivalent resistance 5.97 Ω is 11.99V5.97 Ω=2.01A .

Then the potential difference across the equivalent resistance 2.67 Ω is 2.01A×2.67 Ω=5.36 V . The current in the resistor 8.0 Ω is 5.36V8.0 Ω=0.67A

Conclusion:

Therefore, the current through the resistor of resistance 8.0 Ω is 0.67A .

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