Kirchhoff's voltage law (KVL)

Also known as the Loop rule · Kirchhoff's second law.

The algebraic sum of all voltage rises and drops around any closed loop in a circuit is zero.

V − I·R₁ − I·R₂ = 0 around the loop: the source rise equals the sum of the drops.

ΣV(loop) = 0

V: each source rise or component drop around the loop (volts)

In plain English: Walk any complete loop and the volts gained from sources exactly equal the volts dropped across components — like returning to the same floor after a walk up and down stairs.

Where you'll meet it: Voltage dividers, working out the drop left over for an LED after its resistor, and mesh analysis. If your loop doesn't sum to zero on paper, you've missed a drop.

Calculators that use this law

Circuit SolverR_series = R₁ + R₂ + …Voltage Divider CalculatorV_out = V_in × R₂ / (R₁ + R₂)Reverse Voltage Divider CalculatorR₂ / (R₁ + R₂) = V_out / V_in Kirchhoff's Laws Calculator (KCL & KVL)KCL: ΣI_in = ΣI_out Wheatstone Bridge CalculatorAt balance: P / Q = R / X → X = (Q × R) / P Thévenin and Norton Equivalent CalculatorV_th = open-circuit voltage Zener Diode Regulator CalculatorR_s = (V_in − V_z) / (I_load + I_z(min))

Components this law governs

Potentiometer / Rheostat / TrimmerWired as a potentiometer it is a voltage divider: the wiper voltage is the source share the two halves of the track split between them.Photoresistor (LDR)Almost always wired in a divider with a fixed resistor, so the loop sums to the supply and the junction voltage is your light reading.555 Timer ICThe internal three-resistor chain divides the supply into the ⅓ and ⅔ thresholds the comparators watch — a divider, so the loop must sum.Rectifier DiodeThat drop is a real term in the loop: a 5 V supply after a rectifier is 4.3 V, and in a bridge you lose two drops.Zener DiodeThe series resistor and the zener share the supply: R must drop (Vin − Vz) at the worst-case current, or regulation collapses.Bridge RectifierTwo diodes conduct in series each half-cycle, so the DC output is the peak minus two forward drops — about 1.4 V lost before you start.

More in Circuit analysis — Kirchhoff's laws

Kirchhoff's current law (KCL)