# In a Wheatstone’s bridge, three resistance P,Q  and R  connected in the three arms and the fourth arm is formed by two resistance S1 and S2  connected in parallel. The condition for bridge to be balanced will be Option 1) $\frac{P}{Q}= \frac{R}{S_{1}+S_{2}}$ Option 2) $\frac{P}{Q}= \frac{2R}{S_{1}+S_{2}}$ Option 3) $\frac{P}{Q}= \frac{R\left ( S_{1}+S_{2} \right )}{S_{1}S_{2}}$ Option 4) $\frac{P}{Q}= \frac{R\left ( S_{1}+S_{2} \right )}{2S_{1}S_{2}}$

As we learnt in

Wheat stone Bridge -

It is an arrangement of four resistances which can be used to measure one of them in terms of rest

- wherein

We know that $\frac{P}{Q}=\frac{R}{S}$

$\because S =\frac{S_{1} \ S_{2}}{S_{1} + S_{2}}$

$\therefore \frac{P}{Q} =\frac{R\left ( S_{1}+S_{2} \right )}{S_{1} \ S_{2}}$

Option 1)

$\frac{P}{Q}= \frac{R}{S_{1}+S_{2}}$

This is incorrect.

Option 2)

$\frac{P}{Q}= \frac{2R}{S_{1}+S_{2}}$

This is incorrect.

Option 3)

$\frac{P}{Q}= \frac{R\left ( S_{1}+S_{2} \right )}{S_{1}S_{2}}$

This is correct.

Option 4)

$\frac{P}{Q}= \frac{R\left ( S_{1}+S_{2} \right )}{2S_{1}S_{2}}$

This is incorrect.

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