Question

In a balanced metre bridge, 5 Ω is connected in the left gap and R Ω in the right gap. When R Ω is shunted with equal resistance, the new balance point is at 1.6 I₁ where 'I₁' is the earlier balancing length. The value of 'I₁' is ______ 

Options

• 25 cm

• 35 cm

• 30 cm

• 40 cm

Answer 1

In a balanced metre bridge, 5 Ω is connected in the left gap and R Ω in the right gap. When R Ω is shunted with equal resistance, the new balance point is at 1.6 I₁ where 'I₁' is the earlier balancing length. The value of 'I₁' is 25 cm.

Explanation:

`5/R = ℓ_1/(100 - ℓ_1)` ................(1)

`5/((R/2)) = (1.6ℓ_1)/(100 - 1.6ℓ_1)`

 `10/R = (1.6ℓ_1)/(100 - 1.6ℓ_1)` ................(2)

Dividing Eq(1) by Eq(2)

`5/10 = ℓ_1/(100 - ℓ_1) xx (100 - 1.6ℓ_1)/(1.6ℓ_1)`

`1/2 = (100 - 1.6ℓ_1)/((100 - ℓ_1) xx 1.6)`

200 - 3.2 ℓ₁ = 160 - 1.6 ℓ₁

1.6 ℓ₁ = 40

∴ `ℓ_1 = 40/1.6 = 25  cm`