Kirchhoff's Current Law
Current into a junction equals current out of it (charge conservation).
Formula
Variables
Example
If 3 A and 2 A flow into a junction, exactly 5 A must flow out.
How it works
Kirchhoff's Current Law says that at any electrical junction, the total current arriving must equal the total current leaving. This works because electric charge is conserved: charge cannot pile up indefinitely at a node, so whatever charge per second flows in must flow out unless the node is storing charge momentarily, which is usually neglected in circuit analysis.
When to use it
Use this law when analyzing circuit nodes, especially in resistor networks, mesh-node problems, and circuits with multiple branches. It is one of the main tools for finding unknown currents in DC and low-frequency AC circuits.
Worked example, step by step
At a node, 4.5 A flows in through one branch and 1.8 A flows in through another branch. Two branches carry current out: one with 3.1 A and one unknown. Step 1: Write KCL: total current in = total current out Step 2: 4.5 A + 1.8 A = 3.1 A + I_unknown Step 3: 6.3 A = 3.1 A + I_unknown Step 4: I_unknown = 6.3 A - 3.1 A Step 5: I_unknown = 3.2 A Final answer: the unknown outgoing current is 3.2 A.
Common mistakes to avoid
- Forgetting to include every branch connected to the node
- Mixing up current directions and adding incoming and outgoing currents with the same sign
- Using KCL when charge is accumulating at the node without stating that the circuit is in steady state
Did You Know?
Kirchhoff's current law is simply conservation of charge — what flows into a junction must flow out.
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