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8.6 Electrical power
The rate at which energy is transferred is known as power. Power P is measured in watts (W). (If you are
not sure about this, refer back to Chapter 5, where we looked at the concept of power in relation to forces
and work done.)
where P is the power and ΔW is the energy transferred in a time Δt.
Take care not to confuse W for energy transferred or work done with W for watts.
Refer back to the equation derived from the definition of potential difference:
This can be rearranged as:
Thus:
The ratio of charge to time,
, is the current I in the component. Therefore:
P = VI
By substituting from the resistance equation V = IR, we get the alternative equations for power:
KEY EQUATIONS
Equations for power:
WORKED EXAMPLE
6
Calculate the rate at which energy is transferred by a 230 V mains supply that provides a current of
8.0 A to an electric heater.
Step 1 Use the equation for power:
P = VI
with V = 230 V and I = 8.0 A.
Step 2 Substitute values:
P = 8 × 230 = 1840 W (1.84 kW)
7
a
A power station produces 20 MW of power at a voltage of 200 kV. Calculate the current
supplied to the grid cables.
Step 1 Here we have P and V and we have to find I, so we can use P = VI.
Step 2 Rearranging the equation and substituting the values we know gives:
Hint: Remember to convert megawatts into watts and kilovolts into volts.
So, the power station supplies a current of 100 A.
b
The grid cables are 15 km long, with a resistance per unit length of 0.20 Ω km−1. How much
power is wasted as heat in these cables?
Step 1 First, we must calculate the resistance of the cables:
resistance R = 15 km × 0.20 Ω km−1 = 3.0 Ω
Step 2 Now we know I and R and we want to find P. We can use P = I2R:
power wasted as heat,
Hence, of the 20 MW of power produced by the power station, 30 kW is wasted – just
0.15%.
8
A bathroom heater, when connected to a 230 V supply has an output power of 1.0 kW.
Calculate the resistance of the heater.
Step 1 We have P and V and have to find R, so we can use
Step 2 Rearrange the equation and substitute in the known values:
Note: The kilowatts were converted to watts in a similar way to the previous example.
Questions
17 Calculate the current in a 60 W light bulb when it is connected to a 230 V power supply.
18 A power station supplies electrical energy to the grid at a voltage of 25 kV. Calculate the output
power of the station when the current it supplies is 40 kA.
Power and resistance
A current I in a resistor of resistance R transfers energy to it. The resistor dissipates energy heating the
resistor and the surroundings.. The p.d. V across the resistor is given by V = IR. Combining this with the
equation for power, P = VI, gives us two further forms of the equation for power dissipated in the resistor:
Which form of the equation we use in any particular situation depends on the information we have
available to us. This is illustrated in Worked examples 7a and 7b, which relate to a power station and to
the grid cables that lead from it (Figure 8.15).
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