E.m.f. and internal resistance Cambridge International AS & A Level Physics revision
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In plain words
A battery marked 1.5 V rarely gives you the full 1.5 V. The battery itself has some resistance, so some of the energy is wasted inside it, warming it up. The harder you work it, the more is lost, and the lower the voltage at its terminals.
4 things to know
- The e.m.f. ε of a source is the energy it transfers per unit charge in driving charge round the complete circuit. The p.d. across a component is the energy per unit charge transferred in that component.
- A real source has an internal resistance r. ε = I(R + r), and the terminal p.d. is V = ε − Ir. The "lost volts" are Ir.
- With no current, the terminal p.d. equals the e.m.f. As the current rises, the terminal p.d. falls.
- To measure ε and r: vary the external resistance, record the terminal p.d. V and the current I, and plot V against I. The intercept on the V axis is ε and the gradient is −r.
Worked example
A cell of e.m.f. 6.0 V and internal resistance 0.50 Ω is connected to a 5.5 Ω resistor. Find the current and the terminal p.d.
- ε = I(R + r): 6.0 = I × (5.5 + 0.50).
- I = 1.0 A.
- Terminal p.d. = ε − Ir = 6.0 − 1.0 × 0.50 = 5.5 V.
Tips and tricks
- On a graph of terminal p.d. against current, the intercept is the e.m.f. and the gradient is −r.
- A voltmeter across a cell that is supplying no current reads its e.m.f.
It lands in your notebook with its questions as flashcards.
E.m.f. and internal resistance: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
A cell has an e.m.f. of 1.5 V and an internal resistance of 0.50 Ω. What is its terminal p.d. when it supplies 1.0 A?
V = ε − Ir.
What is the e.m.f. of a cell?
It is measured in volts.
On a graph of terminal p.d. against current for a cell, what is the gradient?
V = ε − Ir has the form y = c + mx.
When does the terminal p.d. of a cell equal its e.m.f.?
With no current there are no lost volts.
What are the "lost volts" of a cell?
They are equal to Ir.
Quiz
5 questions
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Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
E.m.f. and internal resistance
Cambridge International AS & A Level Physics 9702 · 8 marks · papermunch.org
Name ______________________________ Date ______________
A battery of e.m.f. 12 V delivers 2.0 A to a lamp, and the p.d. across the lamp is 11 V. Find the internal resistance of the battery.[3]
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0.50 Ω. The lost volts are 1.0 V, and 1.0 ÷ 2.0 = 0.50.
State the difference between e.m.f. and potential difference, in terms of energy.[2]
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E.m.f. is the energy transferred per unit charge from other forms to electrical energy, by the source. Potential difference is the energy transferred per unit charge from electrical energy to other forms, in a component.
A cell of e.m.f. 1.5 V and internal resistance 0.30 Ω is short-circuited with a thick wire. Find the current, and explain why the cell gets hot.[3]
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5.0 A. All of the cell's energy is transferred in its own internal resistance: 7.5 W of heating inside the cell.
Answers: E.m.f. and internal resistance
- 1. 0.50 Ω. The lost volts are 1.0 V, and 1.0 ÷ 2.0 = 0.50.
- 2. E.m.f. is the energy transferred per unit charge from other forms to electrical energy, by the source. Potential difference is the energy transferred per unit charge from electrical energy to other forms, in a component.
- 3. 5.0 A. All of the cell's energy is transferred in its own internal resistance: 7.5 W of heating inside the cell.