Calculating Energy Transfers

Electric current is the rate of flow of electric charge. The equation is:

Q = I t

One coulomb is the charge that passes a point when a current of one ampere flows for one second. In a metal wire the charge is carried by electrons.

The potential difference (p.d.) between two points is the energy transferred per unit charge as charge moves between them. One volt is one joule per coulomb.

E = Q V

A 12 V battery gives 12 J to every coulomb of charge that passes through it. When the charge flows through a lamp, the same 12 J per coulomb is transferred to heat and light.

Substituting Q = I t into E = Q V produces the most useful form for calculations in circuits:

E = I V t

Because P = I V, this is the same as E = P t. If power is in watts and time is in seconds, energy is in joules. If power is in kilowatts and time is in hours, energy is in kilowatt-hours (kWh).

Electricity companies charge for energy in kilowatt-hours, because the joule is too small a unit for household use. One kWh is the energy transferred by a 1 kW appliance running for 1 hour: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.

The cost is

• cost = number of kWh × price per kWh.
• A meter in the home records the number of kWh used.
• To find kWh, multiply power (kW) by time (h).
• Remember that appliances with the largest power rating are not necessarily the most expensive to run: it is the energy, power × time, that counts.

Keep units consistent. If the question gives minutes, change to seconds for E = IVt in joules. If it gives watts, change to kilowatts for kWh. Always write the unit with the final answer. For the effects of the energy transfer, such as heating, see Electricity and Heat.

A battery or power supply is the source of energy. As charge flows round a circuit, it carries energy from the source and transfers it in the components. The total energy transferred by the source equals the total energy transferred in all the components, which is another statement of conservation of energy.

In a series circuit, the same current flows through every component, so the energy transferred in each is shared in proportion to the p.d. across it.

Not all the energy is transferred usefully.

The same ideas can be applied to a motor lifting a load: the electrical energy supplied I V t becomes gravitational potential energy mgh plus some wasted heat.