Resistance, electrical energy and power

Slowing the flow

• Push current through a thin wire and it gets hot; through a thick one, less so.
• Resistance 电阻 measures how hard it is for current to flow.
• It controls the current, heats your toaster, and sets your electricity bill.

Resistance

• Resistance $R$ is measured in ohms 欧姆 ($\Omega$). A bigger resistance gives a smaller current:

• To measure it: an ammeter in series reads $I$, a voltmeter across the component reads $V$, then divide.

A pylon carries the cables that bring electricity at very high voltage

What changes a wire's resistance

• A longer wire has more resistance — resistance is proportional to length ($R \propto l$).
• A thicker wire has less resistance — resistance is inversely proportional to the cross-sectional area ($R \propto \tfrac{1}{A}$).
• So doubling the length doubles $R$; doubling the area halves it.

I-V graphs for a resistor, a filament lamp 灯丝灯泡 and a diode 二极管

Current–voltage graphs

• A fixed resistor 定值电阻: a straight line through the origin — resistance is constant, so $I \propto V$.
• A filament lamp: an S-shape that gets flatter — the wire heats up, so its resistance rises.
• A diode: current one way only — very high resistance the "wrong" way.

Electrical power and energy

• Power is the energy transferred each second, in watts (W):

• The energy transferred in a time $t$, in joules (J), is:

The kilowatt-hour 千瓦时

• Electricity bills use a bigger unit, the kilowatt-hour (kWh): the energy a $1\ \text{kW}$ appliance uses in $1$ hour.

• Example: a $2\ \text{kW}$ heater for $3$ hours uses $6\ \text{kWh}$.

Worked examples

You've got it

Write from a resistance of 9 ohms

• A component has 18 V across it and a current of 2.0 A.
• Find the resistance and the power. A 1.5 kW heater runs for 2.0 hours.