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Topic 4 · 4.2

Charge, current, p.d. and resistance

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Describe positive and negative charge, charging by friction (transfer of electrons), and conductors and insulators; describe electric fields EXTENDED.
  • Know that current is a flow of charge; use ammeters; use \( I = \dfrac{Q}{t} \) and conventional current EXTENDED.
  • Define e.m.f. and p.d.; use voltmeters; use \( E = \dfrac{W}{Q} \) and \( V = \dfrac{W}{Q} \) EXTENDED.
  • Use \( R = \dfrac{V}{I} \); describe the experiment; sketch and explain I–V graphs and use R ∝ L, R ∝ 1/A EXTENDED.
  • Use \( P = IV \) and \( E = IVt \); define the kilowatt-hour and calculate costs.

📚The physics

Electric charge

There are positive and negative charges. Like charges repel; unlike charges attract. Charging a solid by friction involves only the transfer of negative charge (electrons). Charge can be detected with a gold-leaf electroscope or by seeing whether an object attracts small pieces of paper. EXTENDED Charge is measured in coulombs (C).

A polythene rod rubbed with a cloth gains electrons from the cloth, becoming negative, while the cloth becomes positive. Two positive charges repel; a positive and a negative charge attract. Only electrons move when solids are charged by friction.
A charged rod picks up scraps of paper or bends a thin stream of water.

Conductors (metals, graphite) let charge flow because they contain free electrons; insulators (plastic, rubber, glass, dry wood) do not, because their electrons are held in their atoms. To test a material, connect it in a circuit with a cell and a lamp (or ammeter): the lamp lights only for a conductor.

Electric fields EXTENDED

An electric field is a region in which an electric charge experiences a force. The direction of the field at a point is the direction of the force on a positive charge at that point.

Field lines point radially outwards from a positive point charge, radially inwards to a negatively charged conducting sphere, and straight, evenly spaced and parallel from the positive plate to the negative plate between two oppositely charged parallel plates.
EXTENDED Between parallel plates the field is uniform: evenly spaced, parallel lines.

Current, e.m.f. and potential difference

Electric current is a flow of charge; in metals it is the movement of free electrons. It is measured with an ammeter in series (analogue or digital, with different ranges). Direct current (d.c.) flows one way; alternating current (a.c.) keeps reversing.

\[ I = \frac{Q}{t} \]

EXTENDED Current is the charge passing a point per unit time. Conventional current flows from positive to negative; free electrons flow from negative to positive.

  • E.m.f. is the electrical work done by a source in moving a unit charge around a complete circuit, measured in volts (V).
  • Potential difference (p.d.) is the work done by a unit charge passing through a component, in volts, measured with a voltmeter connected in parallel.
  • EXTENDED \( E = \dfrac{W}{Q} \) and \( V = \dfrac{W}{Q} \): 1 V = 1 J/C.

Resistance

\[ R = \frac{V}{I} \]
A circuit to measure resistance: a battery, an ammeter, a variable resistor and the resistor R in series, with a voltmeter connected in parallel across R.
Vary the current with the variable resistor, record V and I, and find R = V/I (or plot V against I).

The resistance of a metal wire increases with its length and decreases as its cross-sectional area increases. EXTENDED R is directly proportional to length and inversely proportional to cross-sectional area: double the length, double R; double the area, half R.

Three current-voltage graphs. A fixed resistor: a straight line through the origin. A filament lamp: an S-shaped curve that flattens at higher voltages in both directions. A diode: no current in reverse and little until about 0.7 V forwards, then a steep rise.
EXTENDED The lamp’s filament gets hotter at higher currents, so its resistance increases.

Electrical energy and power

\[ P = IV \qquad E = IVt \]

Circuits transfer energy from the source (a cell or the mains) to the components and then to the surroundings. The kilowatt-hour (kWh) is the energy transferred by a 1 kW appliance in 1 hour (3.6 × 106 J). Cost = number of kWh × price per kWh.

✏️Worked example

A heater is connected to the 230 V mains. The current is 9.2 A. (Modelled on 0625/32 June 2026 Q8.) (a) Calculate its resistance. [2] (b) Calculate its power. [2] (c) It is used for 3.0 hours a day. Electricity costs Rp 1500 per kWh. Calculate the cost per day. [2] (d) EXTENDED Calculate the charge that flows through it in one minute. [2]

(a) R = V/I = 230 / 9.2 = 25 Ω.

(b) P = IV = 9.2 × 230 = 2100 W (2116 W, about 2.1 kW).

(c) Energy = 2.116 kW × 3.0 h = 6.35 kWh; cost = 6.35 × 1500 = Rp 9500 (9522).

(d) Q = It = 9.2 × 60 = 550 C (552).

Check it. Room heaters are typically 1–3 kW, so 2.1 kW is believable.
Using watts and seconds for the cost. Cost needs kWh: power in kilowatts × time in hours.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Theory.) EXTENDED Complete the definition: an electric field is a region in which … ; and describe the field between two oppositely charged parallel plates. [4] (Modelled on 0625/42 June 2026 Q8(a).)
… an electric charge experiences a force. Between the plates: straight, parallel, evenly spaced lines at right angles to the plates, pointing from the positive plate to the negative plate.
2. (Theory.) EXTENDED A current of 2.5 A flows through a motor for 4.0 minutes. Calculate the charge that flows. [2]
Q = It = 2.5 × 240 = 600 C.
3. (Multiple choice.) A lamp rated 6.0 V, 18 W works normally for 30 s. How much energy does it transfer? A: 3.0 J. B: 108 J. C: 540 J. D: 3240 J.
C. E = Pt = 18 × 30 = 540 J.
4. (Theory.) Explain, in terms of electrons, why a plastic comb becomes negatively charged when it is pulled through dry hair. [2]
Friction transfers electrons (negative charge) from the hair to the comb; the comb has an excess of electrons, so it is negative (the hair is left positive).
5. (Theory.) EXTENDED Sketch the I–V graph for a filament lamp and explain its shape. [3]
A curve through the origin, becoming less steep at higher voltages (symmetrical for negative values). As the current increases the filament gets hotter and its resistance increases, so the current rises less for each extra volt.
6. (Theory.) EXTENDED A wire has a resistance of 12 Ω. What is the resistance of a wire of the same metal that is twice as long and has twice the cross-sectional area? [2]
Twice the length doubles R; twice the area halves it: R = 12 Ω.
7. (Theory.) EXTENDED A battery of e.m.f. 9.0 V drives 40 C of charge round a circuit. Calculate the energy transferred by the battery. [2]
W = EQ = 9.0 × 40 = 360 J.
8. (Theory.) A 1.5 kW kettle is used for 20 minutes each day. Calculate the energy used per week in kWh. [2]
Per day: 1.5 kW × (20/60) h = 0.50 kWh; per week: 0.50 × 7 = 3.5 kWh.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Balloons and Static Electricity” and “Charges and Fields”
  • PhET “Ohm’s Law” and “Resistance in a Wire”