In a Wheatstone bridge, three resistance $P, Q$ and $R$ are connected in the three arms and the fourth arm…

In a Wheatstone bridge, three resistance $P, Q$ and $R$ are connected in the three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced is
  1. $\frac{P}{Q}=\frac{2 R}{S_1+S_2}$
  2. $\frac{P}{Q}=\frac{R\left(S_1+S_2\right)}{2 S_1 S_2}$
  3. $\frac{P}{Q}=\frac{R\left(S_1+S_2\right)}{S_1 S_2}$
  4. $\frac{P}{Q}=\frac{R\left(S_1 S_2\right)}{S_1+S_2}$

Solution

For balanced Wheatstone's bridge we have $\frac{P}{Q}=\frac{R}{S}$ Where $S$ is the equivalent resistance of $S_1$ and $S_2$ in parallel $S=\frac{S_1 S_2}{S_1+S_2}$ $\therefore \frac{P}{Q}=\frac{R\left(S_1+S_2\right)}{S_1 S_2}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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