Electric Power and Energy
Power is the rate of doing work.
Energy or Work Done = power x time
E = P x t
or
P = E/t
or
t = E/P
In an electric circuit, power may also be defined in two other ways:
1. the rate at which energy is used.
2. It is the rate at which electric energy is delivered to a circuit.
3. it is the rate at which an electric circuit does the work of converting the energy of moving electrons into some other form of energy.
The basic unit of power is the watt (W)… named after James Watt a Scottish inventor who lived from 1736 to 1819.
Much of the electrical equipment we use is rated in terms of the power or watts it consumes. E.g. a light bulb is rated as 60 W, 100 W, 200 W, and so on.
Toasters, irons, clothes dryers, and other appliances also have a certain wattage rating.
The power unit is usually given in terms of kilowatts (1,000 watts = 1 kW). Therefore, the energy unit on which most electric companies base their bills is the kilowatthour (kWh).
The power formulas show the relationships between electric power and voltage, current, and resistance in a dc circuit. The basic power formula is:
P = V x I
where P = power in watts
V = voltage in volts
I = current in amperes
P = I x I x R R = resistance in ohms
P = (VxV)/R
Using the power formulas
EXERCISES
1. An electric heater has a resistance of 40 ohms and takes a current of 7.5 A when in operation. Find the energy consumed if the heater is used for 12 hours.
2. A household consumes 120 kWh in 8 hrs. Calculate:
(a) the power rating of equipment used.
(b) how long the equipment can operate if the consumer can only afford to pay for 90 kWh.
3. A DC motor takes 4.5 A when connected to a 120 V supply. Calculate the power supplied to the motor.
4. Calculate the power consumed by an electric kettle if it uses a current of 6.25 A and connected to a supply of 240 V.
5. A 150 V bulb takes 0.4 A when fully bright. Determine the power rating of the bulb.
6. A 20 ohm heater element draws 15 A when connected to the supply. Calculate the power rating of the heater.
7. An electric fan has a resistance of 6 ohms and takes a
current of 7.07 A. Calculate the fan’s power rating.
8. What is the power of an electric iron with a resistance of 48 ohms and a current of 5 A.
9. Calculate the power of a kettle rated at 5 A, 80 ohms.
10. A 40 ohm coil is rated at 120 V. Calculate the power absorbed by the coil when it is energised.
KILOWATTHOUR FORMULA
Energy or Work done = power x time
1 Joule (J) = 1 watt (W) x 1 second (s)
kWh = power (kW) x time (hrs)
Energy cost = kWh used x cost per kWh
NB. 1 unit = 1 kWh
Procedure:
Step 1: Write ALL Data
Step 2: Change all power to kW (divide by 1000 if necessary)
Step 3: Change all times to hours (divide by 60 if necessary)
Step 4: Calculate Total Power used (Power = P1 + P2 + P3 + … + PN)
Step 5: Calculate kWh used (Energy or kWh = power x time) ET = E1 + E2 + E3 + … + EN
Step 6: Calculate Energy cost (Energy cost = kWh x cost per kWh)
Eg. 1) A household powered by a 240 V supply, uses the following appliances for 3 hours per day:
a) one 2 kW air conditioning units
b) two 450 W electric fans
c) one 1500 W electric iron
Calculate:
(a) the energy consumed per day
(b) the energy consumed per week
(c) the energy consumed in 2 weeks
(d) the total cost of operating the appliances for 2 weeks, if electricity costs 45 cents per unit/kWh.
Eg. 2) If electricity costs 65 cents per kWh, find the total cost per week to operate the following appliances as indicated:
a) one 3.5 kW heater for 45 minutes per day
b) two 650 W microwave ovens for 3.5 hours per day
c) one 1080 W toaster for 5 hours per day
Problem 1: The average price of electric energy in a certain town is 6¢ per kwh. Find the cost of operating a 250 watt television set for 1.5 hours.
READING THE kWH METER DIAL
Electric meters are precision measuring devices which record (in units called kilowatt-hours/kWh) how much electricity you use.
One kilowatt-hour (kWh) is 1000 watts of electricity consumed for one hour,
OR
The power required to burn a 100-watt light bulb for 10 hours.
The meter reading is made up of one number from each dial. When the pointer is between two numbers, you read the number it has just passed.
The reading below is 13641 kWh. Meters with four dials are read the same way as a five dial meter.