Kirchhoff's Laws

Kirchhoff's current law is conservation of charge: charge can't pile up at a junction, so whatever current arrives must leave — at node A the trunk current I₁ splits into the branch currents I₂ and I₃, and I₁ = I₂ + I₃ exactly. Kirchhoff's voltage law is conservation of energy: go once around any closed loop and the energy given to each charge by the supply is exactly used up in the voltage drops, so the supply voltage equals the sum of the I·R drops around the loop. Here V = I₁·R₁ + I₂·R₂ around the loop through R₂. Together these two laws let you solve any network, however tangled.

• Try this: Change any resistor and watch the KCL box: I₂ + I₃ always adds back to I₁.
• Try this: Watch the KVL box: the drop across R₁ plus the drop across the branch always equals the supply.
• Try this: Make R₂ much smaller than R₃ — most of the current takes the R₂ branch, but the sum still equals I₁.
• Try this: Increase R₁ — it takes a bigger share of the voltage, leaving less for the branches.