Power (4.2.5)
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Power is defined as the rate at which work is done, or the rate of energy transfer. The SI unit of power is the watt A higher power rating means a device transfers more energy per second:
Where:
- is the power in watts (W),
- is the energy transferred (work done) in joules (J), and
- is the time taken in seconds (s).
One watt is defined as the transfer of one joule of energy per second:
Electrical power is the rate at which electrical energy is transferred within a circuit. The electrical power supplied to a component can be calculated using:
Where:
- is the power in watts (W),
- is the potential difference in volts (V), and
- is the current in amperes (A).
A larger current or potential difference leads to a greater rate of energy transfer.
The electrical power dissipated by a component can be found using:
Substituting this equation with Ohm’s law:
Returns the following:
Where:
- is the power in watts (W),
- is the current in amperes (A), and
- is the resistance in ohms (Ω).
The current is squared, so a small increase in current causes a much larger increase in power dissipation.
This equation is commonly used for resistive heating in components such as heaters and filament lamps.
The electrical power dissipated by a component can also be found using:
Substituting this equation with Ohm’s law:
Returns the following:
Where:
- is the power in watts (W),
- is the potential difference in volts (V), and
- is the resistance in ohms (Ω).
For a fixed resistance, increasing the potential difference causes the power dissipated to increase rapidly because the voltage is squared.
There are three common equations for electrical power. To select the correct electrical power equation, first identify which quantities are given in the question.
These equations are all equivalent, but selecting the correct one first avoids unnecessary rearranging.
Avoid common exam pitfalls such as introducing extra steps or using incorrect formulas. These errors not only waste valuable time but also increase the risk of algebraic or unit mistakes.
A quick check of the given quantities in the question should immediately determine the correct equation.
In a series circuit with two unequal resistors, the current is the same through all components. The power dissipated in a component is given by:
Since the current is the same, the power dissipated in the component is directly proportional to the resistance of the component. Therefore, the component with the larger resistance dissipates more power.
The resistor with the greater resistance converts more electrical energy into heat and transfers it to the environment each second, thereby raising the temperature.
In a parallel circuit with two unequal resistors, the potential difference across each component is the same. The power dissipated in a component is given by:
Since the potential difference is the same, the power dissipated in the component is inversely proportional to the resistance of the component. Therefore, the component with the smaller resistance dissipates more power.
The resistor with the smaller resistance dissipates more power, resulting in a higher rate of electrical energy transfer to the surroundings and consequently, greater heating.
Question walkthrough
Power Dissipated by a Resistor
Convert a resistance from kilohms to ohms and use P = V²/R to calculate the power dissipated across a resistor connected to a battery.
Question walkthrough
Comparing Power Dissipation in Resistors
Identify which resistor in a mixed series-parallel network dissipates the most power, by comparing branch resistances and currents rather than calculating each power value directly.
The energy transferred (work done) is equal to the power multiplied by the time for which the energy is transferred. A system with a higher power transfers more energy each second:
Where:
- is the energy transferred (work done) in joules (J),
- is the power in watts (W), and
- is the time taken in seconds (s).
Electrical power in a circuit is given by:
Substituting this equation with the energy transferred equation:
Returns the following:
Where:
- is the energy transferred (work done) in joules (J),
- is the potential difference in volts (V),
- is current in amperes (A), and
- is time in seconds (s).
This shows energy transferred is proportional to current, voltage, and time.
A higher potential difference, current or time increases the energy transferred.
Electrical power in a circuit is given by:
Substituting this equation with the energy transferred equation:
Returns the following:
Where:
- is the energy transferred (work done) in joules (J),
- is the potential difference in volts (V),
- is current in amperes (A), and
- is time in seconds (s).
Question walkthrough
Comparing Power in Series vs Parallel
Compare the energy transferred by identical bulbs connected in series and in parallel across the same cell, using the potential divider effect and the power formula P = V²/R.
Energy transferred by electrical devices can be measured in joules (J), but in domestic electricity use, it is more convenient to use kilowatt-hours (kWh).
A kilowatt-hour is equivalent to the energy transferred by a device with a power of 1kW operating for 1 hour.
Where:
- is energy in kilowatt-hours (kWh),
- is power in kilowatts (kW), and
- is time in hours (h).
is a large unit of energy used in electricity bills. For example, is roughly the energy to run a vacuum cleaner for one hour, or a laptop for ten hours.
To convert between joules and kilowatt-hours:
This conversion comes from:
It is important to note that the conversion factor between kWh and Joules is not on the given datasheet during your A-level physics exams and must be memorised.
The efficiency of a device is a measure of how much of the total power input is converted into useful power output.
Efficiency is usually expressed as a percentage between 0% and 100%.
A more efficient device transfers a greater proportion of the total power input into useful power output.
For example, LED bulbs are much more efficient at converting electrical energy into light energy (90%) than filament bulbs (5%) because less energy is dissipated as thermal energy and a greater proportion of the electrical energy is transferred usefully as light.
It is impossible for a device to be 100% efficient because some energy is always dissipated to the surroundings.
Question walkthrough
Calculating Electricity Cost from Energy
Convert an amount of energy transferred into kilowatt-hours and use the cost per kWh to calculate the total cost of running a heater.
Question walkthrough
Total Power Input from Efficiency
Rearrange the efficiency equation to calculate the total power input to an electric motor, given its efficiency and useful power output.