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. `kl_(1)` and `kl_(2)`
B. `kl_(1)` and `k(l_(2)-l_(1))`
C. `k_(l_(2)-l_(1))` and `kl_(1)`
D. `k_(1) +k_(2)`

Answer

A

Explanation

When 1 and 2 connected
`R = kl_(1)`
When 1 and 3 connected
`X + R = kl_(2) rArr X = k(l_(2) - l_(1))`