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Meter Bridge

In Wheat ston...

Question

In Wheat stones bridge shown in the figure, galvanometer gives no deflection on pressing the key. The balance condition for the bridge is :

A

\frac{R_{1}}{R_{2}} = \frac{C_{1}}{C_{2}}

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B

\frac{R_{1}}{R_{2}} = \frac{C_{2}}{C_{1}}

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C

\frac{R_{1}}{R_{1} + R_{2}} = \frac{C_{1}}{C_{1} - C_{2}}

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D

\frac{R_{1}}{R_{1} - R_{2}} = \frac{C_{1}}{C_{1} + C_{2}}

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Solution

The correct option is B $\frac{R_{1}}{R_{2}} = \frac{C_{2}}{C_{1}}$
$\Rightarrow V_{B} = V_{D}$
$\Rightarrow V_{A} - V_{B} = V_{A} - V_{D}$ ..........1]

$V_{B} - V_{C} = V_{D} - V_{C}$ ..............2]
Dividing 1] by 2]

$\Rightarrow \frac{V_{A} - V_{B}}{V_{B} - V_{C}} = \frac{V_{A} - V_{D}}{V_{D} - V_{C}}$

$\Rightarrow \frac{I R_{1}}{I R_{2}} = \frac{\frac{Q}{C_{1}}}{\frac{Q}{C_{2}}}$

$\frac{R_{1}}{R_{2}} = \frac{C_{2}}{C_{1}}$

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