Question

With an unknown resistance X in the left gap and a resistance of 30 Ω of the gap of a metre bridge, the null point is obtained at 40 cm from the left end of the wire. Find the unknown resistance. Also, find the shift in the null point when resistance in each gap is shunted by a resistance of 8 Ω.

Answer 1

R = 30 Ω, L_X = 40 cm, L_R = 100 − L_X = 60 cm

With the resistance X in the left gap and R = Ω 30 in the right gap,

`X/R = L_X/L_R`

∴ The unknown resistance is

X = `RL_X/L_R`

= `30 xx 40/60`

= 20 Ω

When the resistance in each gap is shunted by 8 Ω, the resistance in the left gap is

X' = 20 Ω || 8 Ω = `(20 xx 8)/(20 + 8)`

= `160/28`

= `40/7` Ω

and the resistance in the right gap is

R' = 30 Ω || 8 Ω = `(30 xx 8)/(30 + 8) = 240/38 = 120/19 Ω`

∴ `(X')/(R') = (L'_X)/(L'_R)`

∴ `(40//7)/(120//19) = (L'_X)/(100 - L'_X)`

∴ `19/21 = (L'_X)/(100 - L'_X)`

∴ 21L'_X = 1900 − 19L'_X

∴ 40L'_X = 1900

∴ L'_X = `1900/40`

= 47.5 cm

Since L'_X > L_X, the null point shifts to the right by L'_X − L_X = 47.5 − 40 = 7.5 cm.