This topic is the foundation for D.C. Circuits and Practical Electricity. Nearly every Paper 2 electricity question begins with Q = It or R = V ÷ I, so the definitions and formulas here carry into the later chapters.
The notes cover electric charge and how charges interact, electric current and its direction, e.m.f. and potential difference, and resistance and the factors that affect the resistance of a wire.
What these notes cover
- •Electric charge and how charges interact
- •Electric current and Q = It
- •Measuring current with an ammeter
- •Conventional current vs electron flow
- •E.m.f. of a source
- •Potential difference across a component
- •Cells in series
- •Measuring voltage with a voltmeter
- •Resistance and R = V ÷ I
- •Length and cross-sectional area of a wire
- •Temperature and resistance (extension)
- •Common mistakes and exam technique
Key definitions
- Electric charge
- Carried by protons (positive) and electrons (negative). It has the symbol Q and is measured in coulombs (C). A single electron carries about 1.6 × 10⁻¹⁹ C.
- Electric current
- The rate of flow of electric charge, measured in amperes (A). A current of 1 A means 1 C of charge passes a point every second.
- Electromotive force (e.m.f.)
- The work done by the source in driving a unit charge round a complete circuit, measured in volts (V). It is not a force.
- Potential difference (p.d.)
- The work done per unit charge in driving the charge through the component, measured in volts (V).
- Resistance
- The ratio of the potential difference across a component to the current flowing through it, measured in ohms (Ω).
Key formulas
Charge
Q = I × t
Q is charge in coulombs (C), I is current in amperes (A), t is time in seconds (s). Rearranged: I = Q ÷ t and t = Q ÷ I. Convert minutes (× 60) or hours (× 3600) to seconds first.
Voltage (e.m.f. or p.d.)
V = W ÷ Q
W is the work done or energy converted in joules (J), Q is the charge in coulombs (C). Applies to both e.m.f. and p.d.; 1 V = 1 J/C.
Resistance
R = V ÷ I
R is resistance in ohms (Ω), V is the p.d. across the component in volts (V), I is the current through it in amperes (A). Rearranged: I = V ÷ R.
Wire resistance
R ∝ L ÷ A
L is the length and A is the cross-sectional area of the wire. Compares wires of the same material at the same temperature.
Scaling ratio for a wire
new R = old R × (new L ÷ old L) × (old A ÷ new A)
Multiply by the length factor, divide by the area factor.
Cells in series
combined e.m.f. = sum of e.m.f.s of cells facing one way − e.m.f.s of cells facing the opposite way
The longer line of each cell symbol is the positive terminal. Cells connected the same way round add; a reversed cell's e.m.f. is subtracted.
Worked example
A hair dryer draws a steady current of 2.5 A from a 12 V supply for 3.0 minutes. (a) Calculate the charge that flows through the dryer in this time. (b) Calculate the electrical energy converted by the dryer in this time.
- 1(a) Convert the time to seconds before substituting: t = 3.0 × 60 = 180 s.
- 2Using Q = It: Q = 2.5 A × 180 s = 450 C, so the charge that flows is 450 C.
- 3(b) Voltage is energy per unit charge, so rearranging V = W ÷ Q gives W = QV.
- 4W = QV = 450 C × 12 V = 5400 J, so the energy converted is 5400 J, which is 5.40 kJ (3 s.f.).
Watch out: Using 3.0 minutes directly in Q = It gives an answer 60 times too small — convert time to seconds first.
Common mistakes
Direction of current
Wrong: Current flows from negative to positive.
Right: Conventional current flows from the positive terminal to the negative terminal outside the source; it is the electrons that drift from negative to positive. All circuit arrows and rules use conventional current.
E.m.f. is not a force
Wrong: E.m.f. is a force, so it is measured in newtons.
Right: E.m.f. is the work done by the source in driving a unit charge round a complete circuit, so it is measured in volts (1 V = 1 J/C).
Swapping the meters
Wrong: Connecting the ammeter in parallel and the voltmeter in series.
Right: Ammeter in series, voltmeter in parallel. A voltmeter in series almost stops the current, and an ammeter in parallel causes a dangerously large current.
Questions students ask
What is the difference between e.m.f. and potential difference?
E.m.f. belongs to the source: it is the work done by the source in driving a unit charge round a complete circuit, converting non-electrical energy (e.g. chemical) to electrical energy. P.d. belongs to a component: it is the work done per unit charge in driving charge through that component, converting electrical energy to other forms. Both are measured in volts.
How do you use Q = It in physics?
Q is charge in coulombs, I is current in amperes and t is time in seconds. Convert minutes (× 60) or hours (× 3600) to seconds before substituting. Rearrange as I = Q ÷ t or t = Q ÷ I to find current or time.
How do the length and thickness of a wire affect its resistance?
Resistance is directly proportional to length and inversely proportional to cross-sectional area, so R ∝ L ÷ A. In a longer wire the electrons travel a longer distance and make more collisions with the metal ions; in a thicker wire there is more space, so fewer collisions. Doubling the length doubles the resistance, and doubling the area halves it.
Why does the resistance of a metal wire increase when it gets hot?
When the wire heats up, the metal ions vibrate more vigorously about their fixed positions. The drifting electrons then collide with the ions more frequently, so the resistance increases. This is why a filament lamp's resistance rises as it glows brighter.
In the full PDF
- •Diagrams: the Q = It formula triangle, conventional current vs electron flow, cells in series, and electrons drifting through the metal ion lattice
- •Further worked examples on finding current, combined e.m.f. of cells, R = V ÷ I and wire scaling
- •Worked example comparing the energy supplied by a battery with the energy converted in a lamp
- •Full e.m.f. vs p.d. comparison table
- •Remaining common mistakes and exam technique, including the three-step method for wire-resistance answers
- •End-of-topic summary