Kirchhoff’s laws
Kirchhoff’s two laws are the bookkeeping behind all circuit analysis. The current law (KCL) says current flowing into any node equals current flowing out. Charge doesn’t pile up at a junction, and it doesn’t vanish. If 3 mA enters a node and 1 mA leaves on one branch, the other branch carries exactly 2 mA.
The voltage law (KVL) says the voltages around any closed loop sum to zero. Walk any loop through the battery and across each component back to your starting point, and every rise is exactly used up by the drops. It’s conservation of energy in circuit form. A charge that returns to where it started must return to the same potential.
Together with Ohm’s law, these two rules can solve any resistor network: label the unknowns, write KCL at the nodes and KVL around the loops, and do the algebra. In practice you rarely grind through the equations, but every shortcut you’ll ever use, from divider formulas to what a simulator computes, rests on these laws.
Key points
- KCL: current into a node equals current out. Charge is conserved at every junction.
- KVL: voltage rises and drops around any closed loop sum to zero.
- KCL, KVL, and Ohm’s law together can solve any resistive circuit exactly.
- Divider formulas and simulator internals are applications of these same laws.
Practice
0 of 3 answered · Not startedWrong answers just let you try again, and hints are there if you want them. Answering every question first time, without hints, is what earns mastery.
- 1
Three wires meet at a node. 2 A flows in on one and 3 A in on another. What flows out on the third?
- 2
What does Kirchhoff's voltage law state about any closed loop?
- 3
A loop contains a 9 V source and three resistors dropping 3 V and 4 V. What must the third resistor drop?
V
