Lesson 3, Topic 3
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# Electric Power

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### What is Electric Power?

Electric power is the time rate of transfer of energy or time rate of doing work.

Power = $$\frac {Energy \: expended}{time} \\ = \frac{Work \: done}{time}$$

P = $$\frac {IVt}{t}$$

P = IV

But I = $$\frac{V}{R}$$and V = $$\scriptsize IR$$

P = $$\frac {V^2}{R}$$

P = I2R

Electrical power is measured in watts (W) or J/s.

Watt is defined as one joule per second. It is the power that is consumed in an electric circuit when one joule of work is done per second.

Larger units are in kilowatt AND megawatt.

1 kW = 1000w

1 MW = 1000000 W

Note:
a. To change watt to kilowatt, you divide the watt by 1000.
$$\frac{watt}{10^3} = \scriptsize kW$$
e.g ⇒ $$\scriptsize 2W = \normalsize \frac{2}{1000} = \scriptsize 0.002 kW \\ \scriptsize \: or \: 2 \: \times \: 10^{-3} kW$$

b. To change watt to megawatt, you divide the watt by 1000000.
$$\frac{watt}{10^6} = \scriptsize MW$$
e.g ⇒ $$\scriptsize 2W = \normalsize \frac{2}{1000000} = \scriptsize 2 \: \times \: 10^{-6} MW$$

c. To change kilowatt to megawatt, you divide the kilowatt by 1000.
$$\frac{kilowatt}{10^3} = \scriptsize MW$$
e.g ⇒ $$\scriptsize 2kW = \normalsize \frac{2kW}{1000} = \scriptsize 0.002MW \\ \scriptsize \: or \: 2 \: \times \: 10^{-3} MW$$

d. To change kilowatt to watt, you multiply the kilowatt by 1000.
$$\scriptsize watt = kilowatt \: \times \: 10^3$$
e.g ⇒ $$\scriptsize 3kW \: \times \: 10^3 = 3000 W \\ \scriptsize \: or \: 3 \: \times \: 10^3 W$$

e. To change megawatt to watt, you multiply the megawatt by 1000000.
$$\scriptsize watt = MW \: \times \: 10^6$$
e.g ⇒ $$\scriptsize 3MW \: \times \: 10^6 = 3 \: \times \: 10^6 W$$

f. To change megawatt to kilowatt, you multiply the megawatt by 1000.
$$\scriptsize kilowatt = megawatt \: \times \: 10^3$$
e.g ⇒ $$\scriptsize 3MW \: \times \: 10^3 = 3 \: \times \: 10^3 kW$$

Electrical energy is sold in commercial units of kilowatt-hour (kWh)

### What is a kilowatt-hour?

A kilowatt-hour is a way to measure how much energy you’re using in the home.

Kilowatt-hour is defined as the electrical energy used by an electrical appliance when the appliance consumes one kilowatt of energy in one hour.

### Value of 1kWh in Joules:

⇒ $$\scriptsize 1kWh = 1 KW \: \times \: 1 \: hr \\ = \scriptsize 1000\: W \: \times \: \left(\scriptsize 60\:seconds \: \times \: 60 \: minutes \right) \\ = \scriptsize 3600000 \: joules \\ = \scriptsize 3.6 \: \times \: 10^6 J$$

### Example 1

An electric kettle is rated 1000W, 220V, calculate the resistance and current supplied.

Solution: P = 1000W, V = 220V, I = ?

(i) Current supplied;

use the formula: P = IV

make I the subject;

⇒ $$\scriptsize I = \normalsize \frac {P}{V} \\ = \normalsize \frac {1000}{220} \\ = \scriptsize 4.54 A$$

(ii) Resistance;

use the formula: V = IR

make R the subject;

⇒ $$\scriptsize R = \normalsize \frac {V}{I} \\ = \normalsize\frac {220}{4.54}\\ = \scriptsize 49.5 \Omega$$

### Example 2:

A PHCN supplied power to a household is as follows;
40W bulb (6), Freezer (750W) and a TV set, 60W for 8hours. If 1kWh is sold at ₦20.50k, calculate the cost of supplying energy for 8hrs.

Solution:

Bulb = 40W x 6 = 240W

Freezer = 750 x 1  = 750W

TV Set =   60W

Total = 1050W

convert 1050W to kW

⇒ $$\scriptsize 1kW = \normalsize \frac {1050}{1000} \\ = \scriptsize 1.050kW$$

For 8hours;

⇒ 1.050 x 8

= 8.40kWh

Cost of 8 hours  = 8.40 x ₦20.50

= ₦172.20k

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