Electrical Power
In the previous sections of this unit, it has been shown that Energy can be changed from one form into another. Even though the Energy type changed, the total Energy of the system remained constant. This section will cover how quickly Energy is converted from one form into another.
The rate of transfer of Energy is known as the Power. The units for Power are Watts (W) and, the Power of a system can be found using the following formula:-
P = E / t
Where:-
P = Power (W)
E = Energy (J)
t = Time (s)
Example 1 -
A light bulb has a Power rating of 100 W. If the light bulb is used for 10 minutes, what is the total Energy used by the bulb?
P = E / t
E = P x t
E = 100 x (10 x 60)
E = 60000 J
E = 60 kJ
Power in Electrical Circuits
When a current flows through an electrical circuit, Energy is transferred from the battery to the components. In the components, this electrical Energy is converted into other forms, such as heat or light. This flow of Energy around the circuit depends the Voltage and Current within the circuit:-
Increasing Current - Faster flow of Charge and therefore faster Energy flow.
Increasing Voltage - Each unit of Charge has more Energy and therefore more Energy flows through the circuit.
This faster Energy flow means a higher rate of Energy flow - a larger Power.
Power in an electrical circuit can be found using the following formula:-
P = I x V
Where:-
P = Power (W)
I = Current (A)
V = Voltage (V)
Example 2 -
How much Power is used by an Iron if it draws a Current of 5.6 A from a Mains Supply?
P = I x V
P = 5.6 x 230
P = 1280 W
Power and Ohm's Law
By combining the above Formula with Ohm's Law (See Ohm's Law - Unit 2) it is possible to find two more formulae for Power :-
P = I x V V = I x R
By substituting Ohm's Law into the Power formula, the following can be found :-
P = I x ( I x R )
P = I2 x R
By Rearranging Ohm's Law to find I, then substituting into the Power formula, the following can be found:-
P = ( V / R ) x V
P = V2 / R
The four Power formulae can then be used to find Power in a range of circuits:-
P = E/t P = I x V P = I2 x R P = V2/R
A tropical fish tank has a Power rating of 130W and is connected to a Mains Supply. Calculate the following :-
1. The Resistance of the aquarium.
2. The Current flowing through the aquarium.
3. The total Energy used in 1 day.
Resistance :-
P = V2 / R
R = V2 / P
R = ( 2302 ) / 130
R = 407 Ω
Fuse Required :-
P = I x V
I = P / V
I = 130/230
I = 0.57 A
Total Energy :-
P = E / t
E = P x t
E = 130 x ( 1 x 24 x 60 x60 )
E = 11232000 J
E = 11.2 MJ
