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Figure shows a circuit that may be used to compare the resistance R of an unknown resistor with a $100 Ω$ standard. The distance $l$ from one end of the potentiometer slider wire to the balance point are 400 mm and 588 mm when X is connected to Y and Z, respectively. The length of the slide wire is 1.00 m. What is the value of resistance R?

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$147 Ω$

$47 Ω$

$32 Ω$

$68 Ω$

answer is B.

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Detailed Solution

When X is connected to Y, the balance length $l$ is proportional to the potential difference across the resistor. When X is connected to Z, the balance length is proportional to the potential difference across the resistor and resistor R.

$\frac{100 + R}{100} = \frac{588}{400} o r R = 47 Ω$

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