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The amount of electrical that is consumed by an electrical energy can be easily calculated and the cost of electrical energy used for a particular appliance can also be calculated
Electrical energy calculations
The amount of electrical energy transferred to an appliance depends on its power and the length of time it is switched on. The amount of mains electrical energy transferred is measured in kilowatt-hours, kWh. One unit is 1 kWh.
E = P × t
Note that power is measured in kilowatts here instead of the more usual watts. To convert from W to kW you must divide by 1,000.
For example, 1,000 W = 1,000 ÷ 1,000 = 1 kW.
Also note that time is measured in hours here, instead of the more usual seconds. To convert from seconds to hours you must divide by 3,600.
For example, 7,200 s = 7,200 ÷ 3,600 = 2 h.
The most important description of electric energy is ohm’s law. It states that
“At constant temperature, the current through the conductor is directly proportional to the potential difference across the points”
i.e. V α I
And it can also be written as V=IR
Where R is the resistance of the conductor
The formula that links energy and power is:
Energy = Power x Time.
The unit of energy is the joule, the unit of power is the watt, and the unit of time is the second.
If we know the power in watts of an appliance and how many seconds it is used we can calculate the number of joules of electrical energy which have been converted to sortie other form.
E.g. If a 40 watt lamp is turned on for one hour, how many joules of electrical energy have been converted by the lamp?
Energy (w) = Power x Time
Energy = 40 x 3600
= 14,400 joules
Current can be calculated using the formula : I = Q/t, where I is the current. Q is the charge in coulombs ,c and t is the time in seconds, s.
E.g : What is the current if 15C of current passes through the circuit in 3 seconds? I = 15C/3s I= 5 C per second or 5C/s.
Voltage
Remember how we defined voltage as the ‘force’ behind pushing a current through a circuit. So how do we measure Voltage?
V= W/Q
Where V is the voltage/potential difference measured in volts. W is the work done in joules and Q is the current in coulombs.
Using the previous example, what is the voltage of the circuit if the energy transferred is 35J?
V= 35J/15C V=2.33 Volts (J)
Calculate the heat produced by an electric iron, which has a resistance of 30 ohms and takes a current of 3 amperes when it is switched on for 15 seconds.
Energy = Power x Time
Power = I2R
= 32 * 30
= 270 watts
Energy = Power x Time
= 270 x 15
= 4050 joules
