Electricity

What electricity covers

Charge on the move: what a current is, what resistance means, and how to predict the behaviour of any arrangement of components. The unit rewards practice on circuits rather than reading, since the questions are mostly analysis of a given diagram. Potential dividers and internal resistance return in the electronics option.

The main ideas

• Current as a rate of flow of charge, the carriers in a metal and in an electrolyte, and conventional current against electron drift.
• Potential difference as energy per unit charge, resistance defined as V/I, and the drift equation behind a current.
• Current-voltage characteristics of an ohmic conductor, a filament lamp and a diode, with Ohm's law as a special case rather than a general rule.
• Resistivity as a property of the material, and how a metal, a thermistor, an LDR and a superconductor each respond to their surroundings.
• Kirchhoff's two laws as conservation of charge and of energy, with the series and parallel rules that follow.
• Potential dividers, including sensing circuits and the effect of a load.
• Electromotive force with internal resistance, and the graph that measures both.

The equations it turns on

I = ΔQΔt$I = \frac{\Delta Q}{\Delta t}$I = ΔQ/Δt

current as a rate

R = VI$R = \frac{V}{I}$R = V/I

the definition of resistance, valid for every component

ρ = RAL$\rho = \frac{RA}{L}$ρ = RA/L

resistivity, in ohm metres

I = nAvq$I = nAvq$I = nAvq

current from carrier density, area and drift speed

V_out = V_in × R₂R₁ + R₂$V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$V_out = V_in × R_2/(R_1 + R_2)

the output of a two-resistor divider

emf = I(R + r)     V = emf - Ir$\text{emf} = I(R + r) \qquad V = \text{emf} - Ir$emf = I(R + r) V = emf - Ir

a cell with internal resistance

Where it usually goes wrong

• R = V/I is a definition and applies to everything. Ohm's law is the narrower claim that I is proportional to V under constant physical conditions, and only the ohmic conductor obeys it.
• Resistance at a point on a curved characteristic is V divided by I there, not the gradient of the tangent.
• A load across a divider output sits in parallel with one resistor, lowering that resistance and the output with it. Keeping the load large compared with the divider keeps the effect small.
• Terminal pd is not the electromotive force. The two differ by Ir whenever current flows, which is why a graph of terminal pd against current has a gradient of size r.

Where to start

Current, charge and direction first, then characteristics and resistivity as a pair about components. Kirchhoff's laws must come before potential dividers. Leave electromotive force and internal resistance last, since it is the lesson that makes sense of a real cell.