define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit

Practical Circuits: Electromotive Force (e.m.f.) ⚡

What is e.m.f.?

The electromotive force, written as ε, is the energy supplied by a source (like a battery) to each coulomb of charge that moves through it.

Mathematically:

\$\varepsilon = \frac{W}{Q}\$

where W is the work done (energy) in joules and Q is the charge in coulombs.

So, e.m.f. is energy per unit charge.

Units and Typical Values

Analogy: Water Pump & Pipe System 🚰

Think of a battery as a water pump and the circuit as a pipe system.

The pressure difference created by the pump pushes water through the pipe.

Similarly, the e.m.f. creates a “pressure” (voltage) that pushes electrons around the circuit.

Just as the pump’s pressure determines how fast water flows, the e.m.f. determines the current for a given resistance.

Measuring e.m.f. in the Lab 🧪

1. Connect a voltmeter across the terminals of the source.
2. Ensure the voltmeter has very high internal resistance (≈10⁶ Ω) so it draws almost no current.
3. Read the voltage; this is the open‑circuit e.m.f. (ε).
4. For a loaded circuit, add a known resistor and use Ohm’s law to find the current, then calculate ε = V + IR.

Example Problem

A 1.5 V AA battery is connected to a 3 Ω resistor.

What is the current and the power delivered by the battery?

Using Ohm’s law:

\$I = \frac{\varepsilon}{R} = \frac{1.5}{3} = 0.5\ \text{A}\$

Power:

\$P = \varepsilon I = 1.5 \times 0.5 = 0.75\ \text{W}\$

Exam Tips for A‑Level Physics 📏

• Remember that e.m.f. is measured with no current flowing (open‑circuit). When a load is connected, the terminal voltage drops below ε.
• Use the formula ε = V + IR when a resistor is present.
• Always check units: volts for ε, amperes for I, ohms for R, watts for power.
• In diagrams, label the direction of conventional current (from + to –). The e.m.f. arrow points from the negative to the positive terminal.
• For multiple sources in series, ε_total = ε₁ + ε₂ + …
• For sources in parallel, ε_total is the same as each individual source (provided they are identical).

Quick Recap 🔍

- e.m.f. (ε) = energy per unit charge (J C⁻¹).

- Measured in volts (V).

- Drives current in a circuit just like a pump drives water.

- Use ε = V + IR for circuits with resistive loads.

- Keep the exam tips handy to avoid common mistakes!