Question

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance Ω is ______.

Options

• 12

• 24

• 36 

• 48

Answer 1

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at 40 cm from left end. A 30 Ω resistance is connected in series with the smaller of the two resistances, the null point shifts by 20 cm to the right end. The value of smaller resistance Ω is 24.

Explanation:

From question, 1_X = 40cm, I_R = 60cm.

using principle of metre-bridge,

`"X"/"R"="I"_"X"/"I"_"R"=40/60=2/3`        ...(i)

When 30Ω resistance is connected in series with the smaller of the two resistances

`("X"+30)/"R"=60/40=3/2`

⇒ R = `(2("X"+30))/3`          ...(ii)

From eqs. (i) and (ii),

`"X"/(2(("X"+30)/3))=2/3`

 ⇒ `(3"X")/(2("X"+30))=2/3`

or, 9X = 4X + 120 ⇒ 5X = 120

∴ X = 24Ω