Lessons · Engineering · Kirchhoff's voltage law
Kirchhoff's voltage law: round any loop, the volts add to zero
Going once around a closed loop, the rises through sources and the drops across resistors sum to zero: ΣV = 0.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
What it is for
A control loop has a 24 V supply, a fuse, a relay coil and a long cable, and the relay will not pull in. Adding the drops around the loop shows where the volts went, and that is the whole of fault-finding by meter.
How to think about it
Pick a direction and go round once. A source you pass from minus to plus is a rise; a resistor passed in the direction of the current is a drop of I × R. Set the sum to zero and solve for the one current.
Worked example
Around any closed loop the voltages add to zero: ΣV = 0The law.
A 10 V source, then 2 Ω and 3 Ω in seriesOne loop, one current.
10 − I × 2 − I × 3 = 0 → I = 10 / 5 = 2 ARise through the source, drops across each resistor, in the direction of travel.
V across the 3 Ω = 2 × 3 = 6 V; across the 2 Ω = 4 V; 6 + 4 = 10 OKThe drops add up to the source, as they must.
Your turn
A 9 V source with 1 Ω and 7 Ω in series. Write the loop equation.
9 − I × 1 − I × = 0
Solve one, graded on the server
The trap
Losing a sign. A second source facing the other way is a drop, not a rise, and adding it instead of subtracting can double the current. Go round in one direction and never change your mind halfway.