Electrical Power

When an electrical current does work against electrical resistance:
- Electrical energy is dissipated as thermal energy in the surroundings
- The heat that is produced will dissipate via thermal conduction, convection and radiation
The amount of heat produced depends on two factors:
- Current: The greater the current, the more heat that is produced
- Resistance: The higher the resistance, the greater the amount of heat produced (for a given current)

Note that reducing the resistance can cause the current to increase
- This could actually increase the amount of heat produced

In mechanics, power P is defined as the rate of doing work
- The potential difference is the work done per unit charge
- Current is the rate of flow of charge
Therefore, the electrical power is defined as the rate of change of work done:

$P = \frac{E}{t} = \frac{W}{t}$

Where:
- P = power (W)
- E = energy transferred (J)
- W = work done (J)
- t = time (s)

The work done is the energy transferred so the power is the energy transferred per second in an electrical component

The power dissipated (produced) by an electrical device can also be written as

$P = I V$

Where:
- I = current (A)
- V = potential difference (V)

Using Ohm's Law V = IR to rearrange for either V or I and substituting into the power equation, means power can be written in terms of resistance R

$P = I^{2} R = \frac{V^{2}}{R}$

Where R = resistance (Ω)
This means that, for a given resistor, doubling the current (or voltage) will yield an electrical power four times greater

Rearranging the energy and power equation, the energy transferred can be written as:

$E = V I t$

Worked example

Two lamps are connected in series to a 150 V power supply. WE - power question image, downloadable AS & A Level Physics revision notes Which statement most accurately describes what happens?

A. Both lamps light normally

B. The 15 V lamp blows

C. Only the 41 W lamp lights

D. Both lamps light at less than their normal brightness

ANSWER: A

Worked example - power (2), downloadable AS & A Level Physics revision notes

Examiner Tip

You can use the mnemonic “Twinkle Twinkle Little Star, Power equals I squared R” to remember whether to multiply or divide by resistance in the power equations, although they are all given in your data booklet.

The most appropriate equation to use will depend on whether the value of current or voltage has been given in the question

Electrical Power (SL IB Physics)

Revision Note