Question

A resistance of 20 Ω is connected in the left gap of a meter bridge and an unknown resistance greater than 20 Ω is connected in the right gap. When these resistances are interchanged, the balance point shifts by 20 cm. The unknown resistance is ______.

Options

• 40 Ω

• 35 Ω

• 30 Ω

• 25 Ω

Answer 1

A resistance of 20 Ω is connected in the left gap of a meter bridge and an unknown resistance greater than 20 Ω is connected in the right gap. When these resistances are interchanged, the balance point shifts by 20 cm. The unknown resistance is 30 Ω.

Explanation:

Balanced condition in meter bridge is given by,

`P/Q = l/(100 - l)`

Here, P = 20Ω

⇒ `20/Q = l/(100 - l)` ............(i)

When resistances are interchanged. l' = l + 20

⇒ `Q/20 = l^'/(100 - l^') = (l + 20)/(100 - (l + 20))` .......(ii)

Multiplying Eqs. (i) and (ii), we get,

`1 = (l/(100 - l))((l + 20))/((80 - l))`

⇒ 100 × 80 - 100l - 80l + l² = l² + 20l

⇒ `l = (100 xx 80)/200 = 40` cm

From Eq. (i), we get,

Q = `60/40 xx 20 = 30Omega`