Question

A metre bridge circuit, with resistance X and R connected in the gaps, gives a balance length of l , from the end where X is connected. When a resistance of 5 P is connected in parallel with X and another resistance of 15 Q is connected in parallel with R, the balancing length remained the same. The ratio of P to Q, in terms of l , is

(1) \(\frac{3l}{(100-3l)}\)

(2) \(\frac{l}{(100-3l)}\)

(3) \(\frac{l}{(300-l)}\)

(4) \(\frac{3l}{(100-l)}\)

Answer 1

(4) \(\frac{3l}{(100-l)}\)

Given \(\frac{x}{R}=\frac{l}{100-l}\)

When 5 P is connected is parallel with X, the effective resistance in Gap 1 is \(\frac{x\times5p}{x+5p}\)

When 15 Q is connected in parallel with R, the effective resistance in Gap 2 is \(\frac{R\times15Q}{R+15Q}\)

Since balancing length remains same,

Alternatively: Since the balacing length is the same, potential drops across the gaps remain the same. Therefore, the ratio of resistances would be the same along individual paths.