The Potential Staircase

A charge starts at the supply p.d. and steps down to 0 V, giving up energy across each resistor. The volts split between R1 and R2 but always add back to the supply — that is Kirchhoff's loop rule, and it proves voltage is energy per coulomb.

Current I = V ÷ (R1 + R2)

1.000 A

12 V ÷ 12 Ω

Potential drops V1 = I·R1 · V2 = I·R2

across R1

4.000 V

across R2

8.000 V

V1 + V2 = 12.000 V = supply

Energy each resistor takes W = Q·V

W1 in R1

4.000 J

W2 in R2

8.000 J

Energy per coulomb = 12.000 J/C — equals the supply p.d.

Supply p.d. V12 V

Resistance R14 Ω

Resistance R28 Ω

Charge moved Q1.0 C

Series circuit · one current everywhere · V1 + V2 = V (loop rule) · energy per coulomb = W ÷ Q = V

Try it: drag Charge Q and watch W1, W2 scale while every voltage stays frozen — voltage is not "used up".