Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 25, Problem 76P

(a)

To determine

The equivalent resistance between a and b .

(a)

Expert Solution
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Answer to Problem 76P

The equivalent resistance of the circuit is 4.10Ω .

Explanation of Solution

Formula used:

The expression for equivalent resistance in upper wire is given by,

  Req,1=R6+(R2+R4)(R4)(R2+R4)+R4

The expression for equivalent resistance in lower wire for is given by,

  Req,2=R822R8+R4

The expression for net equivalent resistance is given by,

  Req=Req,1Req,2Req,1+Req,2

Calculation:

The equivalent resistance in upper wire is calculated as,

  Req,1=R6+( R 2 + R 4 )( R 4 )( R 2 + R 4 )+R4=6Ω+( 2Ω+4Ω)( 4Ω)( 2Ω+4Ω)+( 4Ω)=8.4Ω

The equivalent resistance in lower wire is calculated as,

  Req,2=R822R8+R4= ( 8Ω )22( 8Ω)+4Ω=4Ω+4Ω=8Ω

The net equivalent resistance of the circuit is calculated as,

  Req=R eq,1R eq,2R eq,1+R eq,2=( 8.4Ω)( 8Ω)( 8.4Ω)+( 8Ω)=4.10Ω

Conclusion:

Therefore, the equivalent resistance of the circuit is 4.10Ω .

(b)

To determine

The current in each resistor.

(b)

Expert Solution
Check Mark

Answer to Problem 76P

The currents through upper wire 6Ω resistor, lower wire 4Ω resistor, 4Ω resistor parallel with 2Ω and 4Ω resistors, upper wire 6Ω

  =(4Ω+2Ω) resistor and, lower wire in parallel 8Ω resistor are 1.43A , 1.50A , 0.86A , 0.57A and 0.75A respectively.

Explanation of Solution

Formula used:

The expression for current in upper wire 6Ω resistor is given by,

  I6=VReq,1

The expression for current in upper wire 4Ω resistor is given by,

  I4=V(I6)(R6)R4

The expression for current in upper wire 6Ω resistor is given by,

  I6,upper=V(I6)(R6)R6

The expression for current in lower wire is given by,

  Ilower=VReq,2

The expression for current in lower wire in parallel 8Ω resistor is given by,

  I8=V(I lower)(R4)R8

Calculation:

The current in upper wire 6Ω resistor is calculated as,

  I6=VR eq,1=12.0V8.4Ω=1.43A

The current in upper wire 4Ω resistor is calculated as,

  I4=V( I 6 )( R 6 )R4=12.0V( 1.43A)( 6Ω)4Ω=0.86A

The current in upper wire 6Ω resistor is calculated as,

  I6,upper=V( I 6 )( R 6 )R6=12.0V( 1.43A)( 6Ω)6Ω=0.57A

The current in lower wire is calculated as,

  Ilower=VR eq,2=12.0V8Ω=1.5A

The current in lower wire in parallel 8Ω resistor is calculated as,

  I8=V( I lower )( R 4 )R8=12.0V( 1.5A)( 4Ω)8Ω=0.75A

Conclusion:

Therefore, the currents through upper wire 6Ω resistor, lower wire 4Ω resistor, 4Ω resistor parallel with 2Ω and 4Ω resistors, upper wire 6Ω =(4Ω+2Ω) resistor and, lower wire in parallel 8Ω resistor are 1.43A , 1.50A , 0.86A , 0.57A and 0.75A respectively.

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Chapter 25 Solutions

Physics for Scientists and Engineers

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