Learn the basics of Electrical Engineering.

Kirchhoff's Current Law

The sum of currents flowing towards any node is equal to the sum of nodes flowing away from it.

Kirchhoff's current law is a basic law of Electrical Engineering which explains the relationship of current at any node.
kirchhoffs-current-law

Example 1: A circuit with 9 resistors.

A circuit with 9 resistors is provided. There are 9 different values of current. Find the unknown values and parameters in the circuit.
example-1-kirchhoffs-current-law
Solution: 
Step 1: Apply the KCL at node a:
Now I_1 + I_2 = I_3
5 A + I_2 = 10 A
or I_2 = 10 A - 5 A
= 5 A

Step 2: At node b apply the KCL
I_3 = I_4 + I_5 + I_6
or I_5 = I_3 - I_5 - I_6
= 10 A - 5 A - 2 A
= 3 A

Step 3: At node c by the application of KCL
I_7 = I_4 + I_5 + I_6
or I_7 = 2 A + 5 A + 3 A
= 10 A

Step 4: At node d from KCL
I_7 = I_10 + I_9
or I_10 = I_7 - I_9
= 10 A - 1 A
= 9 A

Example 2: Application of Ohm's Law + KCL

Find all the unknown current in this circuit.
ohmlaw-and-kcl-example-2
Solution: 
Step 1: Using the Ohm's law find the current I_1
I_1 = 20 V / 10 ohm = 2 A

Step 2: Applying KCL we get 
I_1 = I_2 + I_3
or I_3 = 2 A - 0.5 A = 1.5 A

Step 3: Again apply KCL at second node we get:
I_2 + I_3 = I_4
or 0.5 A + 1.5 A = I_4
or I_4 = 2 A

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