State the Krichhoff's law of electric network. In the figure shown $P = 2 ohms Q = 4 ohms, R = 4 ohms$ and $S = 2 ohms$ . Resistance between $C$ and $D$ is $1 ohms$ . Find the current through each resistance.

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Solution

By applying the equilibrium condition of wheat stone bridge we get

In loop ACDA

$2 I_{1} + 2 I_{g} - 4 I_{2} = 0$

In loop CBDC

$4 (I_{1} - I_{g}) + 2 (I_{2} + I_{g}) - 2 I_{g} = 0$

In loop ADBA

$4 I_{1} + 2 (I_{2} + I_{g}) = 2$

On solving the above three equation we get

$I_{1} = \frac{1}{7}$

$I_{2} = \frac{4}{7}$

$I_{g} = \frac{3}{7}$

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