Energy and power in electric circuits

Heating up wires

As electrons flow through wires, they collide with the ions in the wire which causes the ions to vibrate more. This increased vibration of the ions increases the temperature of the wire. Energy has been transferred from the chemical energy store of the battery into the internal energy store of the wire.

The amount of energy transferred each second (power) between the energy stores can be calculated using the equation:

power = current × potential difference

\[P=I \times V\]

This is when:

One watt is equal to one joule per second (J/s).

Power can also be written as:

power = current2 × resistance

\[P = I^2 \times R\]

This is when:

  • power (P) is measured in watts (W)
  • current (I) is measured in amps (A)
  • resistance (R) is measured in ohms (Ω)


How much energy is transferred each second by a current of 2 amps (A) driven by a potential difference of 230 volts (V)?

\[P = I \times V\]

\[P = 2 \times 230\]

\[P = 460~ W\]


What power is dissipated by a current of 3 A through a 10 Ω resistor?

\[P = I^2 \times R\]

\[P = 3^2 \times 10\]

\[P = 9 \times 10\]

\[P = 90~W\]

Efficient transmission of power

Energy can be transferred by an electrical current; any electrical appliance needs to be given enough energy every second. Electrical power can be delivered as a low current with a high voltage, or a high current with a low voltage.

power = current2 × resistance

The equation shows that a high current will have a much higher heating effect on the transmission wires than a low current. For this reason, transmitting energy at a high voltage with a low current will keep the wires cooler and waste less energy.

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