1. Overview
This topic explores how energy is transferred into and out of an electrical circuit. Understanding the difference between electromotive force (e.m.f.) and potential difference (p.d.) is essential for calculating how much energy a power source provides and how much energy components like lamps or motors consume.
Key Definitions
- Electromotive Force (e.m.f.): The electrical work done by a source (such as a cell or generator) in moving a unit charge around a complete circuit.
- Potential Difference (p.d.): The work done by a unit charge passing through a specific component.
- Volt (V): The unit of measurement for both e.m.f. and p.d. One volt is equivalent to one joule of work done per coulomb of charge ($1 V = 1 J/C$).
- Voltmeter: A device used to measure the p.d. between two points or the e.m.f. of a source.
Core Content
Understanding e.m.f. vs. p.d.
While both are measured in Volts, they represent different sides of energy transfer:
- e.m.f. represents the energy supplied to the charges by the battery/cell.
- p.d. represents the energy used (dissipated) by the charges as they pass through components like resistors or bulbs.
Measuring Voltage
To measure the p.d. across a component, a voltmeter must be connected in parallel with that component.
- Analogue Voltmeters: Use a needle and scale. They require the user to look directly at the scale to avoid parallax errors and to choose the correct range (e.g., 0-5V or 0-15V) to get an accurate reading.
- Digital Voltmeters: Provide a direct numerical readout. They are generally more accurate and easier to read, as they automatically handle range adjustments in many cases (auto-ranging).
A simple circuit showing a cell connected to a lamp. A voltmeter is connected in parallel across the lamp to measure p.d., and another voltmeter is connected in parallel across the cell to measure e.m.f.
Voltmeters with Different Ranges
- When using a voltmeter, always start with the highest range if the voltage is unknown to prevent damaging the meter.
- If the reading is small, switch to a lower range to increase the precision of the measurement.
Extended Content (Extended Curriculum Only)
Calculating e.m.f. and p.d.
The relationship between work done ($W$), charge ($Q$), and voltage ($V$ or $\varepsilon$) is defined by the amount of energy transferred per unit of charge.
The Equation for e.m.f.: $$\varepsilon = \frac{W}{Q}$$ Where:
- $\varepsilon$ = electromotive force (V)
- $W$ = Work done/Energy transferred to the charge by the source (J)
- $Q$ = Charge (C)
The Equation for p.d.: $$V = \frac{W}{Q}$$ Where:
- $V$ = potential difference (V)
- $W$ = Work done/Energy transferred by the charge to the component (J)
- $Q$ = Charge (C)
Worked Example
Question: A battery does 12 J of work to move 2 C of charge around a circuit. Calculate the e.m.f. of the battery. Solution:
- Identify the variables: $W = 12\text{ J}$, $Q = 2\text{ C}$
- Use the formula: $\varepsilon = W / Q$
- Calculate: $\varepsilon = 12 / 2 = 6$
- Answer: $6\text{ V}$
Key Equations
| Equation | Symbols | Units |
|---|---|---|
| $\varepsilon = \frac{W}{Q}$ | $\varepsilon$ = e.m.f., $W$ = Work, $Q$ = Charge | $V$ (Volts), $J$ (Joules), $C$ (Coulombs) |
| $V = \frac{W}{Q}$ | $V$ = p.d., $W$ = Work, $Q$ = Charge | $V$ (Volts), $J$ (Joules), $C$ (Coulombs) |
| $V = I \times R$ | $V$ = p.d., $I$ = Current, $R$ = Resistance | $V$ (Volts), $A$ (Amperes), $\Omega$ (Ohms) |
Common Mistakes to Avoid
- ❌ Wrong: Using Joules ($J$) as the unit for e.m.f. or p.d.
- ✅ Right: Always use Volts ($V$). Joules is the unit for Work Done/Energy, not the potential difference itself.
- ❌ Wrong: Thinking that if you decrease the resistance of one component in a loop, the total current stays the same.
- ✅ Right: Decreasing the resistance of any component in a series circuit increases the total current in the entire loop.
- ❌ Wrong: Dividing resistance by voltage ($R/V$) to find current.
- ✅ Right: Use the formula $I = V / R$. Always check your algebraic rearrangement.
- ❌ Wrong: Forgetting to convert milli-units (like $mV$) into standard units ($V$) before calculating.
- ✅ Right: Always convert to standard SI units (e.g., $100\text{ mV} = 0.1\text{ V}$) before plugging numbers into equations.
Exam Tips
- Work vs. Voltage: If a question asks for the definition of e.m.f. or p.d., ensure you include the phrase "per unit charge." Simply saying "work done" will not get the mark.
- Voltmeter Placement: In circuit diagrams, always draw the voltmeter in a separate "loop" around the component you are measuring (parallel). If you draw it in the main line (series), the circuit will not work because voltmeters have very high resistance.
- Energy Transfer Direction: Remember that e.m.f. is about energy entering the circuit (chemical $\rightarrow$ electrical) and p.d. is about energy leaving the circuit (electrical $\rightarrow$ heat/light).