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Kirchhoff's Current Law

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Kirchhoff's Current Law — KCL

The beginner version is wonderfully simple:

Current in = current out

Another way to think of this

At a road junction, cars do not simply vanish. If six cars per minute arrive and two take one branch, four must take the other branch. Electric charge is conserved in the same way.

What is really happening?

A node is a connection point shared by circuit branches. Kirchhoff's Current Law says the algebraic sum of currents at a node is zero. That is another way of saying that charge cannot continuously accumulate at an ordinary steady-state junction.

ΣI = 0

Where did the name come from?

Gustav Robert Kirchhoff (1824–1887) was a German physicist who formulated his circuit laws in 1845 while still a young man. His current and voltage laws became basic tools for analyzing electrical networks.

Worked example

6 A enters. One branch takes 2 A.

6 A = 2 A + I₂

I₂ = 4 A

Try these yourself

6 A enters a junction. One branch carries 2 A. How much must leave through the other branch? 2 A 3 A 4 A 8 A

Current entering must equal current leaving. 6 A = 2 A + 4 A.

Which statement best describes Kirchhoff's Current Law? Voltage is always 120 V Current entering a node equals current leaving it All resistors have equal current Power equals resistance

KCL is an expression of conservation of electric charge at a node.

3 A and 5 A enter a node. One 2 A branch leaves. What current must leave through the final branch? 3 A 5 A 6 A 10 A

Total entering is 8 A. If 2 A leaves one branch, the other must carry 6 A.

A little deeper

In formal analysis, we choose a sign convention. Currents entering a node may be treated as positive and currents leaving as negative, or the reverse. Either convention works when used consistently.

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