3.5.1.1–2ElectricityFoundation

Charge, Current and Potential Difference

Every circuit calculation you’ll ever do at A-Level rests on four linked ideas: $charge$ flowing, the $current$ that flow represents, the $potential difference$ that drives it, and the $resistance$ that opposes it. Get comfortable with how these connect — including what’s actually happening to the electrons inside the wire — and every later circuits lesson becomes far more straightforward.

40 min Video by Science Shorts 3.5.1 Current electricity

Electricity - Charge, Current, PD & Resistance — A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Define electric current as the rate of flow of charge, $I = \frac{Δ Q}{Δ t}$
Use the mean drift velocity equation $I = n A v q$
Define potential difference as energy transferred per unit charge
State Ohm’s law and interpret I–V characteristic graphs for a resistor, filament lamp and diode
Calculate electrical power and energy using $P = I V$ , $P = I^{2} R$ and $P = \frac{V ^{2}}{R}$

Charge, current and drift velocity

$Electric current$ is the rate of flow of electric charge past a point. By convention, current flows from + to − around a circuit (the direction positive charge would move), even though in a metal it is actually negatively-charged electrons drifting the other way.

Inside a conductor, current is carried by a huge number of charge carriers drifting slowly through the material — their $mean drift velocity$ , $v$ , is typically only a fraction of a millimetre per second, even though the electrical signal itself travels at close to the speed of light. The current depends on the number density of charge carriers $n$ (per m³), the conductor’s cross-sectional area $A$ , their drift velocity $v$ , and the charge on each carrier $q$ .

I = \frac{Δ Q}{Δ t} I = n A v q

Current from charge flow rate, and from the microscopic drift velocity equation.

1Use

I = \frac{Δ Q}{Δ t}

I = \frac{15}{5.0}

Answer

I = 3.0

Tip — A thinner wire carrying the same current needs a faster drift velocity, since A is smaller — this is why I = nAvq is often used to explain why a wire narrows at a junction changes the drift speed, not the current.

Potential difference, resistance and Ohm’s law

The $potential difference$ (p.d.) between two points is the energy transferred per unit charge as charge moves between them: a p.d. of 1 volt means 1 joule of energy is transferred for every coulomb of charge that passes. $Resistance$ measures how much a component opposes current flow for a given p.d.

$Ohm’s law$ states that, for a conductor at constant temperature, the current through it is directly proportional to the potential difference across it. A component that obeys this is called $ohmic$ .

V = \frac{W}{Q} R = \frac{V}{I}

Potential difference (V = energy ÷ charge) and the definition of resistance.

1Use

R = \frac{V}{I}

R = \frac{6.0}{0.40}

Answer

R = 15 Ω

I–V characteristics

Plotting current against potential difference for a component reveals how its resistance behaves. A $fixed resistor$ at constant temperature gives a straight line through the origin — constant resistance, obeying Ohm’s law exactly, in both directions (positive and negative p.d. give proportional, oppositely-signed currents).

A $filament lamp$ gives a curve that flattens out as p.d. increases: as current increases, the filament heats up, its ions vibrate more, and electrons collide with them more often — increasing resistance, so the current rises more slowly than a straight proportional line would suggest. A $diode$ conducts current in essentially only one direction: almost zero current in reverse bias, and (once past a threshold voltage, around 0.6 V for silicon) a very rapid rise in current in forward bias — its resistance is enormously high in one direction and low in the other.

Tip — On an I–V graph, resistance at any point is V/I — NOT simply the gradient. For a curved characteristic, the gradient (dI/dV) instead tells you how resistance is changing, not its actual value at that point.

Electrical power and energy

Since p.d. is energy transferred per unit charge and current is charge flow rate, multiplying them gives the rate of energy transfer — electrical $power$ . Combined with $V = I R$ , this gives two further equivalent forms, each useful depending on which quantities you already know.

P = I V = I^{2} R = \frac{V ^{2}}{R}

Three equivalent forms of electrical power.

1Power:

P = I V = 2.5 \times 12 = 30

2Time in seconds:

3 \times 60 = 180

3Energy:

W = P t = 30 \times 180 = 5400

AnswerP = 30 W, energy transferred = 5400 J (5.4 kJ).

Equation recap

I = \frac{Δ Q}{Δ t}

Current as rate of flow of charge.

I = n A v q

Current from charge-carrier density, area, drift velocity and carrier charge.

V = \frac{W}{Q}, R = \frac{V}{I}

Potential difference and resistance.

P = I V = I^{2} R = \frac{V ^{2}}{R}

Electrical power.

Common mistakes to avoid

Believing electrons travel at close to the speed of light through a wire.

The electrical signal (the change in the field) travels almost instantly, but individual electrons — the charge carriers — drift extremely slowly, typically under a millimetre per second.

Assuming a filament lamp obeys Ohm’s law because it has an I–V graph.

Ohm’s law requires a straight-line, proportional I–V graph. A filament lamp’s curved characteristic (resistance increasing with temperature) means it is non-ohmic.

Reading resistance directly off the gradient of a curved I–V graph.

Resistance at any point is always V/I at that point, not the gradient — the gradient of a curve only shows how resistance is changing.

Key takeaways

Current is the rate of flow of charge: I = ΔQ/Δt, and microscopically I = nAvq.
Potential difference is energy transferred per unit charge; resistance is R = V/I.
Ohm’s law: for a conductor at constant temperature, I ∝ V, giving a straight-line I–V graph through the origin.
A filament lamp curves (resistance rises with temperature); a diode conducts in essentially one direction only, past a threshold voltage.
Electrical power: P = IV = I²R = V²/R.

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Charge, Current and Potential Difference

Every circuit calculation you’ll ever do at A-Level rests on four linked ideas:

charge

flowing, the

current

that flow represents, the

potential difference

that drives it, and the

resistance

that opposes it. Get comfortable with how these connect — including what’s actually happening to the electrons inside the wire — and every later circuits lesson becomes far more straightforward.

40 min Video by Science Shorts 3.5.1 Current electricity