The following figure shows a network of currents, their magnitudes and directions. The current $I$ will be equal to _____.

- 3 A

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3 A

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13 A

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20 A

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Solution

The correct option is D $20 A$
Applying Kirchhoff's first law which states that, the sum of currents entering a particular node or a junction is equal to the sum of currents leaving the same node or junction.
In the figure shown above,
$i_{A} = 12 + 8 = 20 A$ -- (1)
$i_{B} = i_{A} + 3 = 20 + 3 = 23 A$ -- (2)
$i_{D} + 5 = 8 A ⟹ i_{D} = 3 A$ -- (3)
but $i_{D} = 3 A = i_{B} + I = 23 + I$ -- (4)
On solving, we get $I = 23 - 3 = 20 A$ .

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