Learning outcomes
- Define e.m.f. and potential difference as energy per charge.
- Use E = QV.
- Distinguish source voltage from component voltage.
- Connect a voltmeter correctly.
- Predict effects of cells in series and parallel.
7.1 Energy and charge in a circuit
A source transfers energy to charges, and components transfer electrical energy to other stores. The same charge circulates through a complete circuit; what changes is the energy carried per coulomb. Voltage is therefore an energy-per-charge quantity.
One volt means one joule per coulomb. The relation V = E/Q can be rearranged to E = QV. A 6.0 V source gives 6.0 J of energy to each coulomb that passes through it, ideally.
7.2 Electromotive force
Electromotive force, e.m.f., is the energy supplied by a source per unit charge passing through it. Despite its name, e.m.f. is not a force; it is measured in volts. Chemical reactions in a cell, mechanical work in a generator or light in a solar cell can provide the energy.
The terminal potential difference of a real cell may be lower than its e.m.f. when current flows because energy is transferred in the cell’s internal resistance. Detailed internal-resistance calculations are not central here, but the distinction explains why battery voltage can fall under load.
7.3 Potential difference
Potential difference, p.d., across a component is the energy transferred from electrical form per unit charge passing through the component. A lamp with 3.0 V across it transfers 3.0 J per coulomb, mainly to light and internal energy.
In a complete circuit, energy supplied per coulomb by sources equals energy transferred per coulomb by components, allowing for internal losses. This energy statement is the deeper reason why potential differences add around a loop.
7.4 Measuring voltage
A voltmeter is connected in parallel across the two points whose p.d. is required. An ideal voltmeter has extremely high resistance, so it draws negligible current and does not significantly alter the circuit.
For an analogue d.c. voltmeter, correct polarity prevents reverse deflection. Start with a range above the expected value, then choose a lower safe range for improved precision. Record the unit and avoid parallax.
7.5 Cells in series
When cells are connected in series with the same orientation, their e.m.f.s add. Three 1.5 V cells ideally provide 4.5 V. If one cell is reversed, its e.m.f. opposes the others and the resultant is reduced.
Series cells can drive a larger current through a given resistance because the total e.m.f. is greater. However, components must be rated for the resulting voltage and current.
7.6 Cells in parallel
Identical cells connected in parallel with matching polarity provide approximately the same e.m.f. as one cell, but can supply current for longer or share a larger current. Cells of different e.m.f. should not be connected directly in parallel because large circulating currents may occur.
Parallel arrangements are useful when capacity and current capability matter more than voltage. The practical behaviour also depends on internal resistance and cell condition.
Worked examples
Energy transferred
A charge of 25 C passes through a lamp with p.d. 12 V. E = QV = 25 × 12 = 300 J.
Charge from energy
A source supplies 900 J at 6.0 V. Q = E/V = 900/6.0 = 150 C.
Cell combination
Four 1.5 V cells in series give 6.0 V if all face the same way. If one is reversed, resultant e.m.f. is 1.5 + 1.5 + 1.5 − 1.5 = 3.0 V.
Practical focus
Investigation
Measure the open-circuit voltage of one cell, two cells in series and two identical cells in parallel. Then connect a fixed resistor and measure terminal voltage under load. Use the same meter range and observe correct polarity.
Examination guidance
- e.m.f. and p.d. are measured in volts, not newtons.
- Use “energy per unit charge”.
- Voltmeter in parallel; ammeter in series.
- Series cell voltages add only when orientations agree.
Check your understanding
- Define e.m.f.
- How much energy is transferred when 8 C passes through 9 V?
- Why does an ideal voltmeter have high resistance?
Answers
- Energy supplied by a source per unit charge.
- E = 8 × 9 = 72 J.
- So it takes negligible current and does not change the circuit significantly.
