Which one of the following equations is valid for the circuit shown below?

I_{3} + I_{5} - I_{6} + I_{7} = 0

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I_{3} - I_{5} + I_{6} + I_{7} = 0

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I_{3} + I_{5} + I_{6} + I_{7} = 0

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I_{3} + I_{5} + I_{6} - I_{7} = 0

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Solution

The correct option is D $I_{3} + I_{5} + I_{6} - I_{7} = 0$
By applying KCL at node A,

$I_{3} + I_{5} = I_{4}$ ...(i)

and at node B,

$I_{4} + I_{6} = I_{7}$

$\Rightarrow I_{4} = I_{7} - I_{6}$ ...(ii)

From equation (i) and (ii)

$I_{3} + I_{5} = I_{7} - I_{6}$

$I_{3} + I_{5} + I_{6} - I_{7} = 0$

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