In the following circuit, if I1 = 10 A, I2 = 15 A and I3 = 20 A, find the total current IT

F2 Madhuri Engineering 11.07.2022 D1 V2

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NHPC JE Electrical 5 April 2022 (Shift 1) Official Paper
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  1. 25 A
  2. 5 A
  3. 15 A
  4. 45 A

Answer (Detailed Solution Below)

Option 3 : 15 A
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Detailed Solution

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Kirchhoff’s Current Law (KCL): It states that the algebraic sum of currents entering a node or closed boundary is zero.

Mathematically, KCL implies that

\(\mathop \sum \limits_{n = 1}^N {i_n} = 0 \)

Where N is the number of branches connected to the node

And in is the nth current entering or leaving the node.

By this law current entering a node may be regarded as positive and current leaving a node may be regarded as negative or vice-versa.

Considered the node in the figure shown below, in which i1, i3, and i5 are incoming current and i2, i4, and i6 are outgoing current.

F12 Jai Prakash 2-2-2021 Swati D1

Applying KCL gives,

i1 + i3 + i5 = i2 + i4 + i6

Hence, the sum of currents entering a node is equal to the sum of the currents leaving the node.

Note: KCL is based on the conservation of charge.

Application:

F2 Madhuri Engineering 11.07.2022 D1 V2

Applying KCL to the circuit,

IT + I2 = I1 + I3

Given,

I1 = 10 A, I2 = 15 A and I3 = 20 A

Hence,

IT = 10 + 20 - 15 = 15 A

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