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}}

 

Answers (1)
V Vakul

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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