What are Kirchhoff's Laws?
Kirchhoff's Laws are two fundamental rules for analyzing electrical circuits: the Current Law (KCL) and the Voltage Law (KVL). Together they let engineers solve for unknown currents and voltages in any circuit, no matter how complex.
Kirchhoff's Current Law (KCL) states the sum of currents entering a node equals the sum leaving it. Kirchhoff's Voltage Law (KVL) states the sum of voltage drops around any closed loop equals zero.
- •Applies at a node (junction)
- •ΣI entering = ΣI leaving
- •Based on conservation of charge
- •Used in nodal analysis
- •Applies around a closed loop
- •ΣV around the loop = 0
- •Based on conservation of energy
- •Used in mesh (loop) analysis
Try it: interactive calculator
Step-by-step worked examples
At a node, currents I1 = 4A and I2 = 6A enter, and one current I3 leaves. Find I3.
KCL: ΣIin = ΣIout 4 + 6 = I3 I3 = 10 A
A loop has a 12V battery and two resistors dropping 5V and 7V. Verify KVL around the loop.
ΣV = 0 12 − 5 − 7 = 0 0 = 0 ✓ KVL confirmed
A loop has an EMF of 9V, one resistor drops 3V, another drops 2V, and a third resistor R2 has an unknown drop. Find R2's voltage drop.
ΣV = 0 9 − 3 − R2 − 2 = 0 R2 = 9 − 3 − 2 = 4 V
Flashcards
Quick quiz
Q1.Two currents enter a node: 3A and 5A. One current leaves the node. What is its value?
Q2.A loop contains one EMF source of 10V and one resistor. What is the voltage drop across the resistor?
Q3.KCL is based on conservation of...
Q4.KVL is based on conservation of...
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Common mistakes
Confusing KCL and KVL. — Correct: KCL applies to currents at a node; KVL applies to voltages around a loop.
Forgetting sign conventions when applying KVL. — Correct: Assign consistent +/− signs as you go around the loop — EMF rises positive, resistor drops negative (or vice versa) — and stay consistent.
Applying KCL to a whole loop instead of a single node. — Correct: KCL applies strictly at nodes (junctions); KVL applies around loops.
Ignoring assumed current directions. — Correct: Assume a direction for each unknown current; if the solved value is negative, the actual current flows the opposite way.
FAQ
What are Kirchhoff's laws?
Two circuit-analysis principles: Kirchhoff's Current Law (charge conservation at a node) and Kirchhoff's Voltage Law (energy conservation around a loop).
What is the formula for Kirchhoff's laws?
KCL: ΣIin = ΣIout at a node. KVL: ΣV = 0 around any closed loop.
What are examples of Kirchhoff's laws?
Finding an unknown branch current at a node using KCL, or an unknown resistor voltage drop in a loop using KVL.
How do you calculate current using Kirchhoff's laws?
Sum all currents entering a node and set it equal to the sum leaving (KCL), then solve for the unknown current.