Classwork Series and Exercises (Physics – SS1): Electrical Energy and Power

Definition of 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

Example

Calculate the work done when a current at 5 Amps flows through a conductor for 10 secs if the p.d applied is 5v.

Solution

I = 5A, V = 5V and t = 10sec

W = IVt

W = 5 x 5 x 10 = 25 x 10 = 250J

Electrical Energy Consumed

Power is consumed in kilowatt-hours (KWh). Meters are calibrated in (KWh) so that 1 KWh is the energy supplied at working rate of 1000watts for 1 hour.

1 hour = (60 x 60) secs = 3600sec

1 Kilowatt = 1000 watts

1KWh = 1 Kilowatt x 1 hour

= 1000 x 60 x 60

= 3600000 Joules (J)

= 3.6MJ

Larger value

Kilowatt = 1000 = 10³watts

Megawatt = 1000000 watts = 10⁶watts

Gigawatt =10⁹watts

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