# (a) Use Kirchhoff's rule to obtain the balance condition in Whetstone bridge. (b)Give one practical application that is based on this principle.

To obtain the balancing condition of Wheatstone bridge;
Applying Kirchoff's loop Rule to ABDA, we have
$I_{1}p+I_{g}G-I_{2}R= 0$
where G is galvanometer resistance.
Now Applying Kirchoff's loop Rule to BCDB.we have

$\left ( I_{1}-I_{g} \right )Q-\left ( I_{2}+I_{g} \right )S-GI_{g}= 0$

when the bridge is balanced, $I_{g}= 0$
then, the equation can be written as:-

$I_{1}p-I_{2}R= 0 \: or\: I_{1}p= I_{2}R----(1)$

$I_{1}Q-I_{2}S= 0 \: or \: I_{1}Q= I_{2}S----(2)$

On dividing equation (1) by (2),we get

$\frac{\not{I}_{1}P}{\not{I}_{1}Q}-\frac{\not{I}_{2}R}{\not{I}_{2}S}= 0$
$\frac{P}{Q}-\frac{R}{S}= 0$
$\frac{P}{Q}= \frac{R}{S},$

Which is the balanced condition of a Wheatstone bridge.
A practical device using the principle of Wheatstone bridge is the meter bridge, which is used to measure an unknown resistance.

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