Question

In a meter bridge experiment, resistance are connected as shown in figure, The balancing length 1, is 55 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 75cm. The value of x is ______.

Options

• `54/12 Omega`

• `20/11 Omega`

• `48/11 Omega`

• `11/48 Omega`

Answer 1

In a meter bridge experiment, resistance are connected as shown in figure, The balancing length 1, is 55 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 75cm. The value of x is `underline(48/11 Omega)`.

Explanation:

For the balance point of meterbridge.

Case - I, when balancing length is 55 cm

`"P"/"Q" = ℓ_1/(100 - ℓ_1) => 3/"Q" = 55/45`

Q = `45/55 xx 3`    ...(i)

Case - II When an unknown resistance x is involved

`("P + x")/"Q" = ℓ_1/(100 - ℓ_1)`

`(3 + x)/"Q" = 75/25 => 3 + x = 75/25 xx "Q"`   ...(ii)

By putting the value of Q from equation (i) in equation (ii)

`3 + x = 75/25 xx (45 xx 3)/55`

x = `81/11 - 3 = (81 - 33)/11 = 48/11 Omega`