Show work detail and ensure correct. In the circuits shown above, a battery with

Question

Show work detail and ensure correct. In the circuits shown above, a battery with a voltage ?Vbat = 9 V is connected to the circuit with resistances R1 = R2 = 80 ohms, unknown resistor R3, and a switch connected to R3.

The volt meter measures the potential difference between the points A and B, ?VAB.

Define ?VO be the reading on the voltmeter when the switch is open and ?VC be the reading on the voltmeter when the switch is closed.

If the ratio (?VC / ?VO) = 0.60, what is the value of the resistance of R3?

Give your answer in ohms to three signficant digits.

Explanation / Answer

With Switch Open ,Voltmeter Reading

Vo=Vbat*(R2/R1+R2) =9*(80/80+80)

Vo=4.5 V

With Switch Close ,Voltmeter reading

Vc =Vbat*(R23/R1+R23) =9*(R23/80+R23)

Vc=9R23/(80+R23)

Given

Vc/Vo =0.6

[9R23/(80+R23)]/4.5 =0.6

9R23/(80+R23) =2.7

80+R23=3.33R23 ohms

R23=34.2857ohms

since R2 and R3 are in parallel

R23=R2*R3/(R2+R3)

34.2857=80R3/(80+R3)

80+R3 =2.3333R3

R3=60 ohms

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