Calculating electric power
To calculate electrical powerThe energy transferred each second, measured in watts (W). Power = work done ÷ time taken. use the equation:
power = potential difference × current
\(P = V I\)
This is when:
- power (P) is measured in watts (W)
- potential difference (V) is measured in volts (V)
- current (I) is measured in amperes – also referred to as amps – (A)
Assuming that a transformerAn electrical device that increases, or decreases, the potential difference (voltage) of an alternating current. is 100 per cent efficient, the following equation can be used to calculate the power output from the transformer:
potential difference across primary coil × current in primary coil = potential difference across secondary coil × current in secondary coil
\(V_s \times I_s = V_p \times I_p\)
Example
A step-down transformer converts 11 500 V into 230 V. The power output is used to run a 2,000 W kettle. Calculate the current flowing in the primary coil.
From \(P = V I\), \(kettle~power = V_s \times I_s = 2,000~W\)
\(V_p \times I_p = V_s \times I_s\)
So \(V_p \times I_p = 2,000~W\)
\(I_p = 2,000 \div 11,500\)
input current, \(I_p = 0.174~A\)
High voltage power transmission
The National GridThe network that connects all of the power stations in the country to make sure that everywhere has access to electricity. carries electricity around Britain. The higher the current in a cable, the greater the energy transferred to the surroundings by heating. This means that high currents waste more energy than low currents.
To reduce energy transfers to the environment, the National Grid uses step-up transformers to increase the voltage from power stations to thousands of volts, which lowers the current in the transmission cables. Step-down transformers are then used to decrease the voltage from the transmission cables, so it is safer to distribute to homes and factories.
Explaining high voltage transmission - Higher
In the National Grid, long distance transmission cables use very high voltages, up to 400,000 V. As shown in the kettle example above, the equation \(P = V I\) means that for a given power transfer, the higher the voltage used, the lower the current needed.
Heat energy wastage through electrical resistance is proportional to the square of the current, as given by the equation \(P = I^2 R\). Reducing the current can create huge reductions in energy lost to the surroundings through resistance.
To maximise these energy savings, cross-country transmission lines use the highest possible voltage, limited by the limit of the electrical insulating properties of air.
