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A potentiometer circuit is set up as shown. The potential gradient, across the potentiometer wire, is k volt/cm and the ammeter, present in the circuit, reads 1.0 A when two way key is switched off. The balance points, when the key between the terminals
(i) 1 and 2
(ii) 1 and 3, is plugged in, are found to be at lengths l1 cm and l2 cm respectively. The magnitudes, of the resistors R and X, in ohms, are then, equal, respectively, to
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- k (l2 – l1) and k l2
- k l1 and k (l2 – l1)
- k (l2 – l1) and k l1
- k l1 and k l2
Correct Option: B
(i)When key between the terminals 1 and 2 is plugged in,
P.D. across R = IR = k l1
⇒ R = k l1 as I = 1A
(ii)When key between terminals 1 and 3 is plugged in,
P.D. across (X + R) = I(X + R) = k l2
⇒ X + R = k l2
∴ X = k (l2 – l1)
∴ R = kl1 and X = k (l2 – l1)
