Physics
Physics
3rd Edition
ISBN: 9781259233616
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 18, Problem 80P

(a)

To determine

Redraw the circuit to measure the voltage across 83.0 kΩ resistor.

(a)

Expert Solution
Check Mark

Answer to Problem 80P

The circuit is redrawn to measure the voltage across 83.0 kΩ resistor and the circuit is shown below.

Explanation of Solution

The voltmeter should be connected in parallel with the resistor to measure the voltage across it.

Conclusion:

The circuit is shown below,

Physics, Chapter 18, Problem 80P , additional homework tip  1

(b)

To determine

Find the voltage across the 83.0 kΩ resistor.

(b)

Expert Solution
Check Mark

Answer to Problem 80P

The voltage across the 83.0 kΩ resistor is 7.36 mV .

Explanation of Solution

The voltmeter is connected in parallel with the 83.0 kΩ resistor. Then assume that the voltmeter has zero resistance. The direction of the current are shown in the below figure.

Physics, Chapter 18, Problem 80P , additional homework tip  2

From Kirchhoff’s junction rule,

I1=I2+I3 (I)

From Kirchhoff’s loop rule for the left mesh,

 9.00 VI1(35 Ω)I2(1.40×103 Ω)=0                                             (II)

From Kirchhoff’s loop rule for the right mesh,

 I2(1.40×103 Ω)I3(16.0×103 Ω)I3(83.0×103 Ω)=0                      (III)

Conclusion:

Solve equation III to get I3

I3=1.40×103 Ω99.0×103 ΩI2=0.01414I2 (IV)

Substitute the above equation in equation I.

I1=I2+0.01414I2=1.01414I2

Substitute the above equation in equation II.

9.00 V1.01414I2(35 Ω)I2(1.40×103 Ω)=0I2=9.00 V1.01414(35 Ω)+1.40×103 Ω=6.27 mA

Substitute the above value in equation IV.

I3=0.01414(6.27 mA)=88.7 μA

Then, the reading on the voltmeter is,

V=IR=(88.7 μA)(83.0 kΩ)=7.36 mV

Therefore, the voltage across the 83.0 kΩ resistor is 7.36 mV.

(c)

To determine

Find the voltage across the 83.0 kΩ resistor.

(c)

Expert Solution
Check Mark

Answer to Problem 80P

The voltage across the 83.0 kΩ resistor is 7.86 mV .

Explanation of Solution

The voltmeter is connected in parallel with the 83.0 kΩ resistor and the voltmeter has the resistance of 1 MΩ. The direction of the current are shown in the below figure.

Physics, Chapter 18, Problem 80P , additional homework tip  3

From Kirchhoff’s loop rule for the right mesh,

 I2(1.40×103 Ω)I3(16.0×103 Ω+(183.0×103 Ω+11.00×106 Ω)1)=0 (V)

Conclusion:

Solve equation V to get I3

I2(1.40×103 Ω)I3(16.0×103 Ω+(183.0×103 Ω+11.00×106 Ω)1)=0

I3=1.40×103 Ω16.0×103 Ω+(183.0×103 Ω+11.00×106 Ω)1I2=0.01511I2 (VI)

Substitute the above equation in equation I.

I1=I2+0.01511I2=1.01511I2

Substitute the above equation in equation II.

9.00 V1.01511I2(35 Ω)I2(1.40×103 Ω)=0I2=9.00 V1.01511(35 Ω)+1.40×103 Ω=6.27 mA

Substitute the above value in equation VI.

I3=1.01511(6.27 mA)=94.7 μA

Then, the reading on the voltmeter is,

V=IR=(94.7 μA)(83.0 kΩ)=7.86 mV

Therefore, the voltage across the 83.0 kΩ resistor is 7.86 mV.

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