A potentiometer circuit is setup 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 point, when the key between the terminals (i) 1 and 2 (ii) 1 and 3, is plugged in, are found to be at lengths `l_(2) cm` and `l_(2) cm` respectively. The magnitudes, of the resistors `R` and `X`, in ohm, are then, equal, respectively, to

Options

A. `k l_1` and `k l_2`
B. `k(l_2 -k l _1)` and `k l_2`
C. `k l_1` and `k(l_2 - l_1)`
D. `k(l_2 - l_1)` and `k l_1`

Answer

C

Explanation

`R = k l_1, R + X = k l_2 rArr X = k (l_2 - l_1)`.