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 K l_(2)`
B. `K l_(1) and K(l_(2)-l_(1))`
C. `K(l_(2)-l_(1)) and K l_(1)`
D. `K l_(1) and K l_(2)`

Answer

b

Explanation

When the key between terminals `1 and 2` is plugged is ,`R` is in the circuit
`V_(1)=IR=1 R=Kl_(1)" "(because I=1A)`
when the key between terminal 1 and 2 is plugged in `R` and `X` both are in the circuit
`V_(2)=U(R+X)=1(R+X)=Kl_(2)`
`V_(2)-V_(1)=R+X-R=X=K(l_(2)-l_(1))`