MCQ Solution: Current Electricity
Figure shows a circuit that may be used to compare the resistance R of an unknown resistor with a 100 ω standard. The distances ll 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?
1) 32 ω
2) 47 ω
3) 68 ω
4) 147 ω
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.
$$\displaystyle \frac{100 + R}{100} = \dfrac{588}{400} $$ or $$R = 47 \omega$$
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