Electrical Energy
Electrical energy is the work done when a quantity of charge moves between two points of potential differences measured in joules.
Work done = Quantity of charge x p.d
V =w/Q
W = QV……………………………………(i)
W = Work done, Q = Quantity of charge, V = p.d. across the terminals and we already know that Q =It
Meaning W = (It)v
W =Itv……………………………………..(ii)
Where I = Current, V = Voltage, T = Time
Since V = IR
W = I (IR)t
= I2Rt……………………………………(iii)
Since I = V/R
W = V2/R2 x Rt
W = V2t/R…………………………………(iv)
Example
Calculate the electrical energy produced by a heater with a voltage supply of 200v, when a current of 10amps passed through it for 5 minutes.
Solution
I = 10amps, V = 220v, t = 5 x 60 300s
W = Ivt = 10 x 220 300
= 660000 joules (j)
= 660KJ
Heating Effect of Electric Energy
When current passes through a wire or a conductor, electrical energy is converted entirely into heat energy. Thus, Joules law of electrical heating states that: The heat developed in a wire is directly proportional to:
(i) Time: for a given resistance and current, i.e, W α t(R, I are constant.
(ii) The square of the current: for a given resistance and time, i.e, W α I2 (R, t are constant)
(iii) The resistance of the wire: for a given constant current and time, i.e W α R (I and t are constant)
Energy conversion
(i) Conversion of electrical energy into mechanical energy i.e, in lifting of a load using an electric motor.
(ii) The conversion of solar energy to electrical and heat energy, as in solar cells, solar heaters, etc.
(iii) The conversion of electrical energy to heat energy, e.g. a solar plate, electrical heater, electric cable, etc.
Electrical Power
Electrical power is the time rate at which the energy is used up. Power is measured in watts (w).
Power = workdone/time =Ivt/t
Then, Power = Iv……………………………….(i)
or Power = I2R…………………………………..(ii)
Power = V2/R………………………………..(iii)
Example
Calculate the power dissipated by a heater of 220V and a resistance of 10 Ohms
Solution:
P = V2/R = 220 x 220/10 = 4840 watts = 4.84 Kilowatt (Kw)
Types of Power
(i) real (ii) apparent (iii) active (iv) reactive power
1. Real Power: This is the power used in driving machines in the factories in which (cos θ) power factor is considered, e.g. induction motor fluorescent, etc.
It is represented as IV cosθ
2. Apparent power: Apparent power is just the power available for any electrical appliance which is simply structured, e.g. a transistor radio, computer, etc.
Power factor = Real power/Apparent power
Power factor = cosθ
Real power = IV cosθ
Apparent power = Real power/power factor
Apparent power = IV cosθ/cosθ
Apparent power = IV
3. Active and reactive power: This is too advanced for this level, but little of it has been dealt with under Simple AC Circuit.
Measurement of Electric Power
Electrical power consumed by an electrical appliance is measured in watt.
Watt is the product of electrical and the p.d between the two points.
1 watt = volts x Ampere
Kilowatts-hour = volt x Ampere/1000 x time (hours)
Horse power is equivalent 746 watts approximated to 750 watts
1 watt = volts x Amperes
Kilowatt hour = power (Kw) x time (hrs)/1000
Kilowatt-hour is the unit of electrical energy watt-hour = volt x Amperes x hours
Watt hour = watts x hours
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