Measuring Electrical Energy
Power and Energy
Power is the rate of work done or energy conversion.
SI unit: watt (W)
Other unit: kilowatts (kW) 1kW = 1000 W
P = VI = V2⁄R = I2R
Hence, we can calculate the work done by the useful electrical energy as
E = Pt = VIt = (V2⁄R)t = I2Rt
Note as there are three formulas for calculating power and electrical energy, which formula to use depend on the given quantities in the question.
However, if comparing the power or electrical energy in series circuit, P = I^(2) R is better as current is the same for series circuit.
If comparing the power of electrical energy in parallel circuit, then P = V^(2) / R is better as potential difference is the same for parallel circuit.
Cost of Electricity
Normally, we calculate the amount of electrical energy used in kilowatt-hours, kWh (meaning to say that kWh is the unit for electricity usage) because the cost of electricity consumed is calculated based on the number of kWh of electrical energy used. i.e 24 cents per kWh in Singapore.
1 kWh = 1kW * 1h
= 1000W * 3600 s
= 3600000 J
Cost of electrical energy = unit cost * the amount of electricity consumed.
Flowchart in finding the total cost:
An electrical iron with a heating element of resistance 60 Ω is connected to the 240 V mains. Calculate
a) the electrical power produced in the heating element
b) the amount of electrical energy consumed when the iron is used for 20 minutes.
c) the cost of the electricity given that Singapore Power charges $0.2565 per kWh.
a) Power = (240)^(2) / 60 = 960 W = 0.96 kW
b) WD = 0.96 x 20/60 = 0.32 kWh
c) Cost of electricity = 0.32 x $0.2565 = $0.08208
= $0.08 (to the nearest cents)
Power Rating v.s Specification
A light bulb with a specification of “240V, 60 W” means
Under normal working conditions, it requires a potential difference of 240V and a power of 60W.
A light bulb has a power rating 60W means
60 Joules of electrical energy is converted to heat and light energy per unit time. (This is linked to the definition of power)
Note that resistance is the only constant when the appliance does not connect to the emf or potential difference required for the appliance to work normally.