Kirchhoff's voltage law
/ KEER-khof /
Kirchhoff's voltage law, KVL, is about loops rather than junctions. Pick any closed loop in a circuit and walk all the way around it back to your starting point. The voltage rises (across sources) and voltage drops (across resistors and other components) you pass must exactly cancel, summing to zero. The everyday picture is a hike that ends where it began: no matter how much you climbed and descended along the way, your net change in altitude is exactly zero, because you are back at the same spot.
Formally, the algebraic sum of all the voltage changes around any closed loop is zero, which is the same as saying the rises equal the drops. The trick is bookkeeping the signs: a source might lift you up by 9 V while resistors drop you back down. For example, in a single loop with a 9 V battery feeding a 600 ohm and a 300 ohm resistor in series, the 6 V and 3 V drops add to 9 V, perfectly balancing the rise. If you measured one drop as 7 V, KVL would tell you the other must be 2 V.
KVL is the second pillar of circuit analysis and the foundation of mesh analysis, and it explains why a voltage divider's drops always add back to the input. At heart it is conservation of energy: voltage is energy per unit charge, and a charge carried once around a loop and back to start cannot have gained or lost net energy. The only common pitfall is sign errors, so always fix a direction to travel the loop and stick to it consistently.
A loop has a 12 V supply, a resistor dropping 8 V, and an LED. KVL says the LED must drop the remaining 12 - 8 = 4 V, because the rises and drops around the loop have to sum to zero.
Around any closed loop, the voltage rises and drops always cancel out.
KVL is conservation of energy around a loop. Almost all mistakes are sign errors, so choose one travel direction and apply it consistently.