Practical Electricity

Measuring Electrical Energy

Electrical Power, P

P = W / t ---(1)

or

P = E / t ---(2)

where,

P - Power in Watts(W)
W - Work done in Joules(J)
E - Energy in Joules(J)
t - time in seconds(s)

V = W / Q ---(3)

where.

V - Potential Difference in Volts(V)
W - Work done in Joules(J)
Q - Charge in Coulombs(C)

From (3)

W = Q x V ---(4)

Substituting (4) into (1)

P = (Q x V) / t ---(5)

Substitute Q = I x t into (5)

P = V x I ---(6)

Substitute V = I x R into (6)

P = I x I x R ---(7)

Substitute I = V / R into (5)

P = (V x V) / R ---(8)

The S.I. unit for Power is Watts(W).

1 Kilowatt = 1000 W
1 megawatt = 1 000 000 W

Electrical Energy, E

From (2)

E = P x t ---(9)

Substitute (6),(7) and (8) into (9)

E = V x I x t = I x I x R x t = (V x V x t) / R

The S.I. unit of Energy is Joule(J).

1 Kilo joule = 1000 J
1 Mega joule = 1 000 000 J

Energy and the Cost

Kilowatt-hours (kWh)

The kilowatt-hour is the common unit used by energy companies to measure electricity. This is a unit of energy not power or time. It is the amount of energy if a 1kW appliance was left on for 1 hour.

The Cost

1kWh of electrical energy costs around 6p, though it may change depending on your supplier. So multiplying the number of Kilowatt-hours you use by the unit cost (approx 6p), give you the total cost of the electricity you use.

Know that:

• an electricity bill will often refer to the electrical energy consumed in terms of units
• One unit in this context is just a shorthand way of saying one kilowatt-hour --> 1 unit = 1kWh.

You should be able to use the formula: cost of electricity used = number of units used × cost of each unit