Electrical Power
A light bulb may be marked 100W
A normal electric fan heater is usually 1 kW
A TV may be rated at 250 W
A small electric motor may run at 5 W
An immersion heater may have a power of 3 kW
An electric clock may have a power of 1 mW
These figures tell you how POWERFUL
the appliance is or much electrical energy it uses in a second. In other words the RATE at
which electrical energy is converted to other forms.
In one second the 100W light bulb
uses 100 J of electrical energy and converts some of it into light energy.
However in one
second the immersion heater uses 3 kW (3000 W) of electrical energy and converts it into heat
energy.
PROBLEM
Put the list below in order, starting with the one that you think is the least powerful.
| (a) electric clock |
(f) calculator |
| (b) freezer |
(g) 60 W bulb |
| (c) television |
(h) stereo |
| (d) electric kettle |
(g) torch |
| (e) immersion heater |
(j) mobile phone |
We know that
electrical energy is given by the equation:
Energy =
Voltage x Current x Time = Voltage x Charge
And
so:
Power = Energy converted/Time = Voltage x Current x Time/Time = Voltage x
current
The formula for electrical power is:
Electrical power = voltage x current
Power = VI
[Power is measured in watts with current in amps and
voltage in volts].
For large amounts of power we use kilowatts kW (1 kW = 1000 W) and
megawatts (1 MW = 1000 000 W). A large power station will operate at over 1000 MW!
Using
Ohm's law (V = IR) we can derive two alternative versions of the power
equation:
ELECTRICAL POWER = VI = I2R = V2/R
Example problems
1. Calculate the electrical power used by an electric motor running from a 240 V supply and taking a current of 0.2 A.
Power = 240 x 0.2 = 48 W
2. Calculate the current drawn from a 12 V battery by a 24 W light bulb.
Current = Power/Time = 24/12 = 2 A
3. Calculate the power of a torch bulb that operates on a current of 60 mA and a voltage of 3 V.
Power = voltage x current = 3 x 0.06 = 0.18 W = 180 mW
4. Calculate the current used by a 3.6 kW immersion heater running at 200 V.
Power = 3600 = 200 x current
Therefore: Current = 3600/200 = 18 A
PROBLEMS
1. What is the electrical power of:
(a) a 12 V electric lamp taking 2.5 A
(b) a 240 V kettle taking 5 A
(c) a 12 V model racing car taking 100 mA
(d) a 12 V heater taking 5 A
(e) a power station producing a current of 500 A at 20 000 V
2. Why would you expect the electrical input power of an electric motor to be more than the output mechanical power?
3. Calculate the currents taken by the following appliances:
(a) a 50 W motor running off 10 V
(b) a 150 mW motor running off 1.5 V
(c) a 2 kW heater running off 200 V
4. Calculate the voltages needed:
(a) 3 kW immersion heater taking 12 A
(b) 60 W heater taking 3 A
5. Calculate the powers of the following:
(a) iron, resistance 50 Ω, current 6A
(b) lamp, resistance 9 Ω, current 3 A
6. Copy and complete the following table:
| 10 |
Voltage (V) |
Current (A) |
Resistance (Ω) |
Power (W) |
| 1 |
6 |
3 |
10 |
10 |
| 2 |
20 |
10 |
10 |
10 |
| 3 |
240 |
0.5 |
10 |
10 |
| 4 |
10 |
5 |
100 |
10 |
| 5 |
10 |
2 |
1200 |
10 |
| 6 |
20 |
10
| 10 |
10 |
| 7 |
10 |
2 |
10 |
1000 |
| 8 |
10 |
3 |
10 |
15 |
| 9 |
12 |
10 |
10 |
24 |
| 10 |
10 |
10 |
2 |
450 |
A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB
