Two different load resistances can receive the same power from a source with internal resistance. A smaller load draws more current and can have a lower terminal voltage. Calculate the power at the load in each case before comparing them.
The 2027 A-Level H2 Physics syllabus (9478) includes the effect of internal resistance on terminal potential difference and output power. This worked example uses the same idealised source model throughout.
- Add the external and internal resistances to find current.
- Use the external resistance in the load-power calculation.
- Compare terminal voltage and power separately.
Worked example | Compare a 1 Ω load and a 4 Ω load
A source has an emf of 12 V and internal resistance of 2 Ω. With a 1 Ω load, the total resistance is 3 Ω and the current is 4 A. The terminal voltage is 4 × 1 = 4 V. The load power is 4² × 1 = 16 W.
With a 4 Ω load, the total resistance is 6 Ω and the current is 2 A. The terminal voltage is 2 × 4 = 8 V. The load power is 2² × 4 = 16 W.
The second load receives the same power at twice the terminal voltage and half the current. Check using P = VI. Both 4 V × 4 A and 8 V × 2 A give 16 W.
Compare the power dissipated inside the source
With the 1 Ω load the internal resistance dissipates 4² × 2 = 32 W. With the 4 Ω load it dissipates 2² × 2 = 8 W. The two output powers match, while the internal losses differ.
Check the power balance. In the first circuit the source supplies 12 × 4 = 48 W, shared between 16 W at the load and 32 W inside the source. In the second it supplies 12 × 2 = 24 W, shared between 16 W and 8 W.
| Load | Current | Terminal voltage | Load power | Internal loss |
|---|---|---|---|---|
| 1 Ω | 4 A | 4 V | 16 W | 32 W |
| 4 Ω | 2 A | 8 V | 16 W | 8 W |
Try a load equal to the internal resistance
A 2 Ω load gives a total resistance of 4 Ω and a current of 3 A. It receives 3² × 2 = 18 W. In this model it receives more power than either of the two loads in the worked example.
Ask a study partner to find the load voltage and internal heating for this third case. The load voltage is 6 V and the internal heating is 18 W. Explain why the two resistors dissipate equal power when their resistances and currents match.
Frequently asked questions
Should I use I²(R + r) for output power?
That gives the total resistive power. Use I²R for the external load alone.
Does the source always deliver the same total power?
In this model the emf stays fixed, while the current and total source power change with the load.
Official information
SEAB’s 2027 A-Level H2 Physics syllabus (9478), Current of Electricity and Circuits. Checked 10 November 2026.