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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