Electric current, potential difference and Ohm's law: WASSCE Physics

Flip a switch and the bulb lights instantly, yet the electrons in the wire crawl along at less than a millimetre a second. Electric current is a flow of charge driven by a potential difference, and Ohm's law ties the two together.

Learning objectives

By the end of this lesson you should be able to:

define electric current, potential difference and e.m.f., with their units
state Ohm's law and use $V = IR$
connect ammeters and voltmeters correctly in a circuit
interpret current–voltage graphs for ohmic and non-ohmic conductors

Electric current

Definition

Electric current is the rate of flow of electric charge:

I = \dfrac{Q}{t}

Its unit is the ampere (A). One ampere is a flow of one coulomb per second (1 A = 1 C s⁻¹).

In metals, current is carried by free electrons, which move from the negative terminal towards the positive. By convention, the direction of conventional current is from positive to negative (the direction positive charge would move).

Worked example

A current of 0.5 A flows through a lamp for 2 minutes. How much charge passes? How many electrons is that? (e = 1.6 × 10⁻¹⁹ C)

Q = It = 0.5 \times 120 = 60\ \text{C} \qquad n = \dfrac{60}{1.6 \times 10^{-19}} = 3.75 \times 10^{20}\ \text{electrons}

\begin{gathered}\begin{aligned}Q &= It \\ &= 0.5 \times 120 \\ &= 60\ \text{C}\end{aligned} \\[6pt] \begin{aligned}n &= \dfrac{60}{1.6 \times 10^{-19}} \\ &= 3.75 \times 10^{20}\ \text{electrons}\end{aligned}\end{gathered}

Potential difference and e.m.f.

Definition

The potential difference (p.d.) between two points in a circuit is the work done (energy converted) per unit charge moving between them: $V = \dfrac{W}{Q}$ . Unit: the volt (1 V = 1 J C⁻¹).

The electromotive force (e.m.f.) $E$ of a cell is the total energy supplied per unit charge that it drives round a complete circuit — equal to the p.d. across its terminals when it supplies no current (open circuit).

The circuit and its meters

A circuit with a cell, a switch, an ammeter in series and a resistor, with a voltmeter connected in parallel across the resistor

Figure 1. The ammeter goes in series; the voltmeter goes in parallel. WASSCE Tutor diagram.

Meter	Measures	Connected	Ideal resistance
Ammeter	current	in series	very low (so it does not reduce the current)
Voltmeter	potential difference	in parallel across the component	very high (so it draws almost no current)

Ohm's law

Definition

Ohm's law: the current flowing through a metallic conductor is directly proportional to the potential difference across its ends, provided the temperature and other physical conditions remain constant.

V = IR

The constant $R$ is the resistance, measured in ohms (Ω): 1 Ω = 1 V A⁻¹.

Worked example

A p.d. of 12 V across a resistor drives a current of 0.4 A. Find its resistance. What current flows if the p.d. is raised to 18 V?

R = \dfrac{V}{I} = \dfrac{12}{0.4} = 30\ \Omega \qquad I = \dfrac{18}{30} = 0.6\ \text{A}

\begin{gathered}\begin{aligned}R &= \dfrac{V}{I} \\ &= \dfrac{12}{0.4} \\ &= 30\ \Omega\end{aligned} \\[6pt] \begin{aligned}I &= \dfrac{18}{30} \\ &= 0.6\ \text{A}\end{aligned}\end{gathered}

Verifying Ohm's law (practical)

Connect a cell (or variable supply), a rheostat, an ammeter and the resistor (e.g. a coil of wire) in series, with a voltmeter across the resistor.
Adjust the rheostat to get different currents; record $I$ and $V$ each time (at least five readings).
Plot $V$ against $I$ . A straight line through the origin verifies Ohm's law; its gradient is $R$ .

Precautions: keep the current small and switch off between readings so the wire does not heat up; check for zero errors on the meters; ensure tight connections.

Current–voltage graphs

Three current-voltage graphs: a straight line through the origin for an ohmic resistor, an S-shaped curve that flattens for a filament lamp, and a curve that rises only for positive voltage for a diode

Figure 2. Ohmic and non-ohmic conductors. WASSCE Tutor diagram.

Component	Graph	Behaviour
Metal wire at constant temperature	straight line through the origin	ohmic: $R$ constant
Filament lamp	curve that flattens	non-ohmic: resistance rises as the filament heats
Semiconductor diode	current only in one direction (above about 0.6 V)	non-ohmic: conducts forward, blocks reverse
Thermistor	current rises more steeply as it warms	resistance falls as temperature rises

Key points

$I = Q/t$ (A); conventional current flows from + to −.
p.d. $V = W/Q$ (V); e.m.f. is the energy per coulomb supplied by the source.
Ammeter in series (low resistance); voltmeter in parallel (high resistance).
Ohm's law: $V = IR$ at constant temperature; $R$ in ohms.
Ohmic conductors give a straight-line I–V graph; lamps and diodes do not.

WASSCE examination focus

WAEC tests this

Define current, p.d. and e.m.f., state Ohm's law (with the condition "temperature constant"), and describe the experiment to verify it with a circuit diagram, graph and precautions. You may be asked to sketch I–V graphs for a wire, a filament lamp and a diode. Calculations with $V = IR$ and $Q = It$ are routine.

Quick check

How is an ammeter connected in a circuit?
A 6 V battery drives 0.2 A through a resistor. Find the resistance.
Why is the I–V graph of a filament lamp curved?

Answers: 1. In series. 2. $R = 6 \div 0.2 = 30$ Ω. 3. As the current increases, the filament gets hotter and its resistance increases.

Electric current, potential difference and Ohm's law

Learning objectives

Electric current

Potential difference and e.m.f.

The circuit and its meters

Ohm's law

Verifying Ohm's law (practical)

Current–voltage graphs

Key points

WASSCE examination focus

Quick check

Keep going with current electricity and ohm's law

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