Electricity
Electricity carries a numerical question almost every year: Ohm's law, series and parallel networks, heating effect, power and the cost of energy.
Rules
Ohm's law V = IR at constant temperature. Resistance R = rho l / A, so a longer or thinner wire has more resistance. Series: R = R1 + R2 + ..., same current, voltages add. Parallel: 1/R = 1/R1 + 1/R2 + ..., same voltage, currents add, which is why domestic appliances are wired in parallel.
Power and heating
P = VI = I squared R = V squared / R; heat H = I squared R t; energy in kWh = power in kW x time in hours. An ammeter goes in series and has low resistance; a voltmeter goes in parallel and has high resistance.
Worked example
A 4 ohm and a 6 ohm resistor are joined in parallel across 12 V. Then 1/R = 1/4 + 1/6 = 5/12, so R = 2.4 ohm. Total current I = 12/2.4 = 5 A. Current in the 4 ohm branch is 12/4 = 3 A and in the 6 ohm branch 2 A; the two add back to 5 A, a useful check on the answer.
Traps
Adding parallel resistances directly; using the total voltage across a single branch in a series-parallel network; forgetting to convert watt-hours to kWh; connecting the ammeter in parallel.