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Current Electricity

13 min read

Resistance and resistivity

The resistance R of a conductor is the ratio of the potential difference V across it to the current I through it: R = V ÷ I. For a uniform wire the resistance is proportional to its length and inversely proportional to its cross-sectional area.

ρ is the resistivity of the material (Ω m): copper 1.7 × 10⁻⁸, aluminium 2.8 × 10⁻⁸, nichrome 1.1 × 10⁻⁶. A thick, short wire of a good conductor has low resistance.
  • resistivity (Ω m)
Ohm’s law graphA graph of current against voltage for a resistor. The line is straight and passes through the origin, so current is proportional to voltage. A steeper line means a smaller resistance.voltage V (volts)current I (A)small Rlarge Rstraight line through 0:I ∝ Vgradient = 1 ÷ R
Open the Ohm's law lab
Measure the current for different voltages across a resistor.
Try itResistance of a wire

Choose the resistivity, length and diameter of a wire. Find its resistance.

Combining resistors

Resistors in series and in parallelTwo resistors one after the other in series, where the total resistance is the sum, and two resistors on separate branches in parallel, where the total resistance is smaller than either.R₁R₂SeriesR = R₁ + R₂bigger than eitherR₁R₂Parallel1/R = 1/R₁ + 1/R₂smaller than either
In series the same current flows through each resistor and the voltages add. In parallel the voltage is the same across each resistor and the currents add.

EMF and internal resistance

The electromotive force (e.m.f.) E of a cell is the energy it gives to each coulomb of charge that passes through it. A real cell has internal resistance r, so when a current I flows, some voltage is lost inside the cell. The terminal p.d. is V = E − Ir. The lost voltage is why a battery’s voltage drops when the current is large.

Worked exampleTerminal voltage

A cell of e.m.f. 1.5 V and internal resistance 0.5 Ω supplies a current of 0.6 A. What is the voltage at its terminals?

  1. Voltage lost inside the cell: Ir = 0.6 × 0.5 = 0.3 V.
  2. V = E − Ir.

Answer: The terminal voltage is 1.2 V.

Electrical energy and power

Power in watts, energy in joules. Domestic energy is measured in kilowatt-hours (kWh): 1 kWh = 3.6 × 10⁶ J.
Try itThe cost of electricity

Choose the power of an appliance, how long it is used and the price of a unit (1 kWh). Find the energy used and the cost.

Domestic wiring and safety

A three-pin plugThe back of a three-pin plug. The brown live wire goes to the right terminal through a fuse, the blue neutral wire goes to the left terminal, and the green and yellow earth wire goes to the long top pin. The cable is held by a grip so that the wires cannot pull out.earthneutrallivefusecable grip
WireColourJob
LiveBrownCarries current to the appliance; at high voltage
NeutralBlueCompletes the circuit
EarthGreen and yellowConnects the metal case to the ground, so a fault current flows to earth and blows the fuse instead of shocking you

A fuse is a thin wire that melts and breaks the circuit if the current is too high. Choose a fuse a little above the normal current (3 A, 5 A or 13 A). A circuit breaker does the same job and can be reset. Switches are placed in the live wire. Never touch electrical equipment with wet hands.

A bigger resistance means a smaller current for the same voltage.
Check yourself A wire is doubled in length. Its resistance…
Check yourself A 2 kW kettle is used for 30 minutes. How much energy is used?
Check yourself Why is the earth wire connected to the metal case of an appliance?

Key terms

Resistivity
A property of a material: the resistance of a 1 m length with a cross-section of 1 m².
e.m.f.
The energy given to each coulomb of charge by a source.
Internal resistance
The resistance of the source itself.
Kilowatt-hour
The energy used by a 1 kW appliance in 1 hour: 3.6 MJ.

Summary

  • R = ρL/A; series: add R; parallel: add reciprocals.
  • Terminal voltage V = E − Ir.
  • P = VI = I²R = V²/R; energy E = Pt; cost = kWh × tariff.
  • Fit a fuse in the live wire and connect the earth wire to metal cases.
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