A potentiometer PQ is set up to compare two resistances as shown in… | JEE Main 2017 (8 Apr, Shift 1)

Q77JEE Main 2017 · 8 APR · SHIFT 1Medium

Potentiometer

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K3 is open. The balance point is at a length $\ell$ 1 cm from P when two way key K3 is plugged in between 2 and 1, while the balance point is at a length $\ell$ 2 cm from P when key K3 is plugged in between 3 and 1. The ratio of two resistances $\frac{R_1}{R_2}$ , is found to be:

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Answer: (d)

Same current $I$ flows through $R_1$ and $R_2$ .
Key between 2 and 1: G measures p.d. across $R_1$ : $IR_1 = kl_1$ .
Key between 3 and 1: G measures p.d. across $R_1+R_2$ : $I(R_1+R_2) = kl_2$ , so $IR_2 = k(l_2-l_1)$ .
$\dfrac{R_1}{R_2} = \dfrac{l_1}{l_2-l_1}$
So the answer is (d) $\dfrac{l_1}{l_2-l_1}$ .

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Potentiometer question from JEE Main 2017 (8 Apr, Shift 1)

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