4.1ElectricityFoundation

Charge, Current and Potential Difference

Every circuit calculation in this module rests on one microscopic picture: a vast number of charge carriers drifting slowly through a conductor. Connect that picture to the everyday quantities of current and potential difference, and every later circuits topic becomes a matter of applying a handful of equations correctly.

35 min Video by Science Shorts Module 4.1 Charge and current

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
Use the mean drift velocity equation $I = n A v q$
Define potential difference as energy transferred per unit charge
Use the relationship between charge, current and time, $Q = I t$

Charge and current

Electric current is the rate of flow of electric charge. By convention, current is taken to flow from positive to negative around a circuit, even though in a metal it is negatively-charged electrons that actually drift the other way.

I = \frac{Δ Q}{Δ t} Q = I t

Current as rate of flow of charge, and the rearranged charge equation.

1Use

Q = I t

Q = 2.5 \times 40

Answer

Q = 100

Mean drift velocity

Inside a conductor, current is carried by a huge number of charge carriers moving with a small mean $drift velocity$ — typically a fraction of a millimetre per second, even though the electrical effect itself propagates almost instantly. The current depends on the number density of charge carriers, the conductor’s cross-sectional area, their drift velocity, and the charge on each carrier.

I = n A v q

n = number density of charge carriers (m⁻³), A = cross-sectional area, v = drift velocity, q = charge per carrier.

1Rearrange

I = n A v q

v = \frac{I}{n A q}

v = \frac{2.0}{8.5 \times 1 0 ^{28} \times 1.5 \times 1 0 ^{- 6} \times 1.60 \times 1 0 ^{- 19}}

Answer

v \approx 9.8 \times 1 0^{- 5}

m s⁻¹

Tip — A narrower section of the same wire, carrying the same current, needs a FASTER drift velocity — since I=nAvq must stay balanced, a smaller A means a larger v is required.

Potential difference

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 transfers 1 joule of energy for every coulomb of charge passing.

V = \frac{W}{Q}

Potential difference = energy transferred ÷ charge.

1Use

V = \frac{W}{Q}

V = \frac{60}{5.0}

Answer

V = 12

Equation recap

I = \frac{Δ Q}{Δ t}

Current as rate of flow of charge.

I = n A v q

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

V = \frac{W}{Q}

Potential difference.

Common mistakes to avoid

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

The electrical effect propagates almost instantly, but individual electrons (the charge carriers) drift extremely slowly — often under a millimetre per second.

Assuming drift velocity is the same in every part of a circuit, whatever the wire’s thickness.

For a fixed current, a thinner section of wire (smaller A) requires a FASTER drift velocity, since I=nAvq must remain balanced.

Confusing potential difference with current.

Potential difference is energy transferred PER UNIT CHARGE; current is the rate of flow of charge itself — they are completely different quantities.

Key takeaways

Current I = ΔQ/Δt = rate of flow of charge; Q = It.
Microscopically, I = nAvq, linking current to charge-carrier density, area, drift velocity and carrier charge.
Potential difference V = W/Q, the energy transferred per unit charge.

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Charge, Current and Potential Difference

35 min Video by Science Shorts Module 4.1 Charge and current