Watch voltage drops add up around a loop (KVL) and currents balance at a node (KCL), with live current flow.
KVL — A Single Loop
KCL — A Junction Node
Current flow Resistor / drop Source Voltage label Node (KCL)
KVL: ΣV = 0
KCL: ΣIin = ΣIout
12 V
12 V
10 Ω
10 Ω
1.0 A
3.0 A
Drag the sliders — every voltage and current updates live. KVL: the sum of all voltage rises and drops around the closed loop is always zero. KCL: the total current entering a node equals the total current leaving it.
Kirchhoff's Voltage Law (KVL)
Σ Vrises = Σ Vdrops or ΣV = 0 (around a closed loop)
Go around the loop in one direction and add every voltage: the total is always zero.
The sources raise the potential; each resistor drops it.
Here two DC sources are in series: Vs1 + Vs2 = VR1 + VR2.
KVL comes from conservation of energy: energy gained from the source is entirely lost across the resistors.
Kirchhoff's Current Law (KCL)
Σ Iin = Σ Iout (at any node)
At a node, the current flowing in equals the current flowing out.
Here two sources feed the node and three loads leave it: I1 + I2 = I3 + I4 + I5.
Charge cannot pile up at a junction, so what arrives must leave.