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

Answer

B

Explanation

(b) The balancing length for `R` (when 1, 2 are connected) be `l_(1)` and balancing length for `R + X` (when 1, 3 is connected is `i_(2)`)
Then `iR = kl_(1)`
and `I (R + X) = kl_(2)`
Given `i= 1 A`
`:. R = kl_(1)`
`R + X = kl_(2)`
Subtracting Eq. (i) from Eq. (ii) we get
`X = k (l_(2) - l_(1))`