Internal resistance of a cell
A real cell has an internal resistance r, so its terminal voltage V = E - Ir falls as current flows. A 12 V cell with r = 1 Ω across 5 Ω drives I = 12 / (5 + 1) = 2 A, and V = 12 - 2 × 1 = 10 V.
Circuit builder
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Equivalent resistance5 Ωbetween A and B
Current2 Aterminal 10 V
Power24 WP = VI
| R | I | V | Power | |
|---|---|---|---|---|
| R₁ | 5 Ω | 2 A | 10 V | 20 W |
Step by step
- One resistor, so Req = 5 Ω
- Current from the cell: I = E / (Req + r) = 12 / (5 + 1) = 2 A
- Terminal voltage: V = E - Ir = 12 - 2 × 1 = 10 V
- Power: P = EI = 12 × 2 = 24 W, of which 4 W heats the cell.
Why it works
- The current through the outside resistance R also passes through the cell's own electrolyte, which has a resistance r.
- The loop rule gives E = IR + Ir, so I = E/(R + r).
- The voltage across the terminals is V = IR = E - Ir.
- On open circuit I = 0 and V = E. The more current is drawn, the lower V falls.
- Measuring E and V with a known R gives r = (E - V)/I = R(E/V - 1).
Internal resistance of a cell: quick answers
What is the internal resistance of a cell?
The resistance of the electrolyte and electrodes inside the cell, which the current must pass through. It wastes some of the emf as heat inside the cell.
Why does the terminal voltage drop when more current is drawn?
Because V = E - Ir and Ir grows with the current. Here 2 A through 1 Ω loses 2 V inside the cell.
Can the terminal voltage be more than the emf?
Yes, while the cell is being charged. The current then flows into the + terminal and V = E + Ir.