Question

In a Wheatstones's bridge, three resistances P, Q and R are connected in the three arms and the fourth arm is informed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced will be

• A. $\frac{P}{Q}=\frac{2R}{S_1+S_2}$
• B. $\frac{P}{Q}=\frac{R(S_1+S_2)}{S_1{S}_2}$
• C. $\frac{P}{Q}=\frac{R(S_1+S_2)}{{2S}_1{S}_2}$
• D. $\frac{P}{Q}=\frac{R}{S_1+S_2}$

Answer 1

Answer: (B)

$\frac{P}{Q}=\frac{R(S_1+S_2)}{S_1{S}_2}$

For balanced Wheatstone's bridge
$\frac{P}{Q}=\frac{R}{S}$

Here, $S=S_1\parallel S_2=\frac{S_1{S}_2}{S_1{+S}_2}$
$\Rightarrow \frac{P}{Q}=\frac{R\left(S_1{+S}_2\right)}{S_1{S}_2}$