A potentiometer circuit is set up as shown. the potential gradient, across the potentiometer wire, i

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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 balence points, when the key between the terminals (i) 1 and 2 (ii) 1 and 3, pluggedin, are found to be at lengths l₁ cm and l₂ cmrespectively. The magnitudes, of the resistors R and X, ohm, are then, equal, respectively, to

Accepted Answer

When two way key is switched of, then the current flowing in the resisitors R and X is
     I = 1          A ..... (i)
When the key between the terminal 1 and 2 is plugged in, then
Potential difference across R = IR = kl₁         ..... (ii)
where k is the potential gradient across the potentiometer wire.
When the key between the terminals 1 and 3 is plugged in, then
Potential difference across (R + X) = I(R + X) = kl₂          ..... (iii)
From equation (ii), we get
R + X =

= kl₂Ω [Using (i)]
X = kl₂ - R
= kl₂ - kl₁ [Using (v)]
= k(l₂ - l₁)Ω

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