Kirchhoff Rules Interactive
Adjust the voltage sources and resistors. The circuit updates instantly so you can see how Kirchhoff's Current Law and Voltage Law describe the same circuit from two viewpoints.
The Two Rules
KCL at a node
All currents entering and leaving one node must balance.
ΣI = 0
KVL around a loop
All voltage rises and drops around a closed loop must balance.
ΣV = 0
Node Voltage
0.00 V
KCL Check
0.000 mA
Dominant Path
R1
KCL at the green node
I1 + I2 + I3 = 0
0 + 0 + 0 = 0 mA
Positive current is defined as leaving the node. A negative value means current is entering the node.
KVL around each side loop
V1 - VR1 - Vnode = 0
V2 - VR2 - Vnode = 0
Each source rise is exactly balanced by resistor drops and the node-to-ground drop.
Quick Check
Estimate the node voltage from the circuit above, then type your answer in volts. Within 0.10 V counts as correct.