Question

In a Wheatstone’s bridge, three resistances P, Q and R connected in the three arms and the fourth arm is formed by two resistances S₁ and S₂ connected in parallel. The condition for the bridge to be balanced will be ______.

Options

• `P/Q = (2R)/(S_1 + S_2)`

• `P/Q = (R(S_1 + S_2))/(S_1S_2)`

• `P/Q = (R(S_1 + S_2))/(2S_1S_2)`

• `P/Q = R/(S_1 + S_2)`

Answer 1

In a Wheatstone’s bridge, three resistances P, Q and R connected in the three arms and the fourth arm is formed by two resistances S₁ and S₂ connected in parallel. The condition for the bridge to be balanced will be `bbunderline(P/Q = (R(S_1 + S_2))/(S_1S_2))`.

Explanation:

The fourth arm consists of two resistances, S1 and S2, connected in parallel. The equivalent resistance (S) for this arm is:

`1/S = 1/(S_1) + 1/(S_2)`

= `(S_1 S_2)/(S_1 + S_2)`

A Wheatstone bridge is balanced when the ratio of the resistances in the first two arms equals the ratio of the resistances in the last two arms:

`P/Q = R/S`   ...(i)

Substitute the value of S into the balance equation (i) we get,

`P/Q = R/((S_1 S_2)/(S_1 + S_2))`

`P?Q = (R(S_1 + S_2))/(S_1S_2)`