Circuits and conductors
Kirchhoff: voltage balance
- where
- signed voltage rises and drops around the closed loop (V)
Explain this equation
Finds a missing voltage around a closed loop from the sum of the other signed rises and drops. Useful for checking supply against the drops round a circuit.
Each V is a voltage change met going round the loop: a rise (such as through a source) or a drop (such as across a resistance), each with its sign. The calculator returns the one missing change that brings the total to zero.
Voltage is energy per coulomb. A charge that goes round a loop and back to its start must end with the same energy, so the rises and drops cancel out.
Sense check: if the known terms add up to −12 V, the missing term is +12 V. In a simple loop the supply rise equals the sum of the drops.
Watch out: keep your signs consistent. Adding all terms as positive magnitudes gives a wrong answer.
Add voltage rises and drops with consistent signs around a closed loop. In a simple resistive loop the supply rise equals the total drops.
This is an energy balance per unit charge. Do not add magnitudes without noting whether each term is a rise or a drop.
Enter your values to see the result.
Common mistake
Using the same sign for all rises and drops.
Limits
Lumped DC circuit with no unmodelled induced emf.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.