Electric charge and current

Charge can be positive, negative or balanced overall

Electric charge, Q, is measured in coulombs (C). An object may have positive charge or negative charge. The sign identifies the kind of charge; it is not a judgement about whether the object is safe.

A neutral object still contains positive and negative charges: their totals balance. In ordinary charging of solid objects, electrons can move from one object to another; the protons remain bound in atomic nuclei. An object that gains electrons becomes negatively charged. Losing electrons leaves a net positive charge.

Worked charge account: two initially neutral objects are rubbed together and electrons move from A to B. A loses negative charge and becomes positive; B gains the same negative charge. The transfer separates charge rather than creating it, so the combined charge remains zero.

Use the signs to predict the interaction

Use the charge account before applying the interaction rule. Two objects that both gain electrons are both negative, so they repel; the objects A and B in the transfer example have opposite net charges, so they attract.

Current is the rate of flow of charge

I = Q / t

Current, I, is measured in amperes (A). One ampere means one coulomb of charge passes a point each second. In a metal, electrons move from the negative terminal towards the positive terminal, while conventional currentis defined in the opposite direction, from positive towards negative.

Imagine counting the charge passing a point in a wire during one second. At a steady current, charge does not accumulate in a lamp: the same charge per second enters and leaves it. A smaller current after the lamp would mean charge was continually piling up there.

Apply Q = It with time in seconds

A current of 0.40 A flows for 3.0 minutes. Convert time first:t = 3.0 × 60 = 180 s. ThenQ = It = 0.40 × 180 = 72 C.

A source supplies energy to the charge

The electromotive force (e.m.f.) of an electrical source is measured in volts (V). It describes the energy supplied per coulomb by the source. Despite its name, e.m.f. is not a mechanical force: a force is measured in newtons, whereas one volt is one joule per coulomb. In a cell, chemical energy is transferred to electrical energy; the cell does not manufacture the circulating charge.

A component transfers energy from the charge

The potential difference (p.d.) across a component is the work done per unit charge in driving charge through the component. It is measured in volts:

V = W / Q

A p.d. of 6.0 V means 6.0 J of energy is transferred for each coulomb that passes through the component. Equivalently, the energy transferred is E = QV (W is another symbol for this work done). Match the voltage to the component whose energy transfer you are calculating; do not automatically substitute the source voltage.

Worked energy account: an ideal 6.0 V source supplies 6.0 J per coulomb. In a series circuit with a 4.0 V p.d. across a motor and 2.0 V across a lamp, each coulomb transfers 4.0 J in the motor and 2.0 J in the lamp. For 3.0 C, those transfers are 12 J and 6 J, adding to the source's 18 J. Charge is conserved while energy is transferred.

Use the voltage and current of the same component

R = V / I

Resistance, R, is measured in ohms (Ω). A component has a p.d. of 9.0 V and a current of 0.30 A. Its resistance isR = 9.0 / 0.30 = 30 Ω.

The voltmeter reading must be across this component and the current must pass through it. Dividing the supply voltage by a branch current generally does not give an individual series component's resistance. One ohm means one volt per ampere.

Compare wires at the same material and temperature

A longer wire gives moving electrons a longer path through the material. A larger cross-sectional area provides more paths alongside one another. Compare one dimension at a time: material and temperature must stay the same, and a length comparison also keeps area fixed.

If diameter doubles, cross-sectional area becomes four times as large, so resistance becomes one quarter when material and length remain unchanged.

Common mistakes

Check your understanding

Worked example: connect current, p.d. and resistance

A charge of 24 C passes through a component in 8.0 s. The component transfers 48 J of energy. Find the current, potential difference and resistance.

1. I = Q/t = 24/8.0 = 3.0 A.
2. V = W/Q = 48/24 = 2.0 V. Each coulomb transfers 2.0 J.
3. R = V/I = 2.0/3.0 = 0.67 Ω to two significant figures.

The important check is that each relationship uses quantities from the same time interval and the same component.

Guided practice

Practise this independently

1. Spheres A and C are positively charged; sphere B is negatively charged. State the interaction between A and B, the interaction between A and C, and the unit of charge.
2. 18 C passes a point in 6.0 s. Calculate the current, then state the directions of conventional current and electron flow in a metal connected to a cell.
3. A current of 0.25 A flows for 8.0 min. Calculate the charge transferred.
4. A source is labelled 9.0 V. State the unit of its e.m.f. A motor transfers 24 J when 4.0 C passes through it; find the p.d. across the motor.
5. A wire carries 0.20 A when the p.d. across it is 6.0 V. Find its resistance. A second wire of the same material and temperature is twice as long and has twice the diameter. Compare its resistance with the first wire.

Try this next

Close the answers and redo questions 3–5 with your own sensible values. If one step is wrong, return to that relationship, explain what each symbol means, and try again.

Practise this topic

The topic check covers charge flow, current and voltage, and resistance. Use the feedback to revisit the matching explanation before trying a fresh question.