Question

Figure shows a circuit that may be used to compare the resistance R of an unknown resistor with a 100 $\omega$ standard. The distances $l$ 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?

• A. 32 $\omega$
• B. 47 $\omega$
• C. 68 $\omega$
• D. 147 $\omega$

Answer 1

Answer: (B)

47 $\omega$

When X is connected to Y, the balance length $l$ is proportional to the potential difference across the 100 $\omega$ resistor. When X is connected to Z, the balance length is proportional to the potential difference across the 100 $\omega$ resistor and resistor R.

$\frac{100+R}{100}=\frac{588}{400}$ or $R=47\omega$