Power in Electrical Circuits
The general definition of power is : Power (W) = Energy transferred (J) / Time taken (s)
1 Volt = 1 Joule per Coulomb.
Potential Difference (Volts) = Energy transferred (J) / charge (Coulombs)
Current = Charge / Time taken (s)
Power = Current x Voltage = (Charge / Time taken) x (Energy transferred / Time taken) = Energy transferred / Time taken
Supply and Use of Electricity
Q1. Explain the use of fuses and circuit breakers in electrical circuits and of fuse rating
A fuse is usually made up of a tin-coated copper wire. When a current exceed the design rating value, the wire will overheat and melt, thus breaking the circuit. It will prevent further damage to the appliance or user. It cannot be reused.
A circuit breaker is usually made up of a reusable spring-loaded type of switch. The function of the circuit breaker is similar to that of the fuse. If a current exceeds the design setting, it will spring open and break the circuit as in a fuse. The device can be reused by resetting the spring-loaded switch.
The fuse rating is the maximum current that the fuse can carry without melting. The fuse rating should be slightly higher than the normal working current of an appliance.
Q2. Explain the need for earthing metal casing and for double insulation.
Earth wire is connected to the metal casing of an electrical appliance. In case of a leakage of current, the user may get an electric shock if the live wire is connected to the metal casing. The earth wire allows the current to flow through it to the ground and protects the user from a fatal electric shock.
Double insulation protects the user of the appliance from an electrical shock by preventing any possibility of the external casing becoming live, thus eliminating the need for an earth connection. Firstly, the electric cable is insulated from the internal components of the appliance. Secondly, the internal metal parts, which could become live if a fault developed is also insulated from the external casing.
Q3. State the meaning of the terms 'live', 'neutral', and 'earth'.
Live wire carries electric current to the appliances.
Neutral wire completes the circuit by forming a path for the current back to the mains. It is usually at zero volts.
Earth wire has very low resistance and is usually connected to the metal casing of the appliances. It forms a safety outlet for current in case the appliance becomes live.
Q4. Explain why switches, fuses and circuit breakers are wired into the live conductors.
They must be fitted onto the live wire so that when the switch is off or when the fuse/circuit breaker is broken, they disconnect the high voltage from the appliances.
1. Which of the following is the reason for a plug to have only two pins?
a. The plug already contains a fuse as safety feature.
b. The appliance is not used in a wet environment.
c. The appliance is well insulated.
d. The conducting wires are thick enough to have a low electrical resistance.
2. When an electrical iron is switched on, the fuse blows immediately. What is the possible reason?
a. The earth wire is disconnected.
b. The live wire and neutral wire connections in the plug are interchanged.
c. The earth wire and neutral wire connections in the plug are interchanged.
d. The live wire touches the metal case of the electrical iron.
3. Lamp X and lamp Y both use tungsten as the filament. The filament of lamp X is thinner and longer than that of lamp Y but both filaments have the same mass. When connected to the mains and switched on, which lamp is brighter and which lamp has a larger resistance?
Brighter Larger resistance
a. X X
b. X Y
c. Y X
d. Y Y
4. An electric kettle is accidentally dropped onto the floor and the impact caused the live wire to make electrical contact with the metal case. The electric kettle is connected to the mains with a proper 3-pin plug. What will happen when the circuit is switched on?
a. The current will flow to the Earth continuously.
b. The circuit will be switched off automatically.
c. The metal case will become live and dangerous.
d. The wires will heat up.
5. An electric kettle is accidentally dropped onto the floor and the impact caused the live wire to make electrical contact with the metal case. The case is earthed and the plug to the electric kettle contained a 4 A fuse. Given that the normal working current for the kettle is 3 A, what will happen when the circuit is switched on?
a. The fuse will not melt and current will flow to the Earth continuously.
b. The fuse will melt and current will flow to the Earth continuously.
c. The fuse will not melt and current will not flow to the Earth continuously.
d. The fuse will melt and current will not flow to the Earth continuously.
6. A kettle has a label stating '240 V, 2.0 A'. The table below shows the maximum current that may be carried safely by wires of different diameters. From the table below, select the smallest diameter of wire which can be safely used for this kettle.
Wire diameter/mm Maximum current/A
a. 0.10 1.0
b. 0.15 2.3
c. 0.20 4.0
d. 0.25 6.3
7. A kettle has a label stating '240 V, 750 W'. The table below shows the maximum current that may be carried safely by wires of different diameters. From the table, select the smallest diameter of wire which can be safely used for this kettle.
Wire diameter/mm Maximum current/A
a. 0.10 1.0
b. 0.15 2.3
c. 0.20 4.0
d. 0.25 6.3
8. What is the use of a fuse?
a. to prevent the current from coming out from the live terminal.
b. to prevent the current from coming out from the neutral terminal.
c. to disconnect the appliance from the high potential.
d. to allow current to discharge to the Earth.
9. The cost of a unit (kWh) of electricity is 10 cents.
appliance power rating time used
lamp 100 W 5 hrs
heater 1.5 kW 3 hrs
cooker 3 kW 0.5 hrs
What is the total cost when all these appliances are used for the times shown?
a. 6.5 cents
b. 65 cents
d. 265 cents
e. 5060 cents
10. An electric cooker has a hotplate rated at 1500 W and an oven rated at 2000 W. During one day, the hotplate is switched on for a total of 1.0 hr and the oven is switched on for 3.0 hrs. The cost of electricity is 24 cents per kWh. What is the cost of using the electric cooker during one day?
a. 56 cents
b. 84 cents
c. 180 cents
d. 336 cents
1. c: 2-pin plug is used when there is no need for the earth wire. An appliance which is well insulated internally and externally does not require earth wire.
2. d: The fuse will only blow when the current flowing through it is higher than the normal operating current. When the live wire touches the metal case of the electrical iron, it is possible that an electrical path is established to the Earth without going through the resistor. A high current will therefore be drawn from the mains and the fuse will thus melt. Choice b and c will still allow the iron to operate normally but with potential danger.
3. c: The resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross-section area of the wire. Filament X is thinner and longer, thus has a larger resistance. The brighter lamp is the one with the higher power. Based on P=V2/R, the one with the lower resistance will be brighter.
4. b: When the live wire touches the metal case, current will flow from the live wire to the Earth via the metal case. The resistance along the path is very low and therefore a high current is drawn from the mains. When a proper 3-pin plug is used, the high current will melt the fuse and create an open circuit to stop the current flow.
5. d: When the live wire touches the metal case, current will flow from the live wire to the Earth via the metal case. The resistance along the flow is very low and so a high current is drawn from the mains. When a proper 3-pin plus is used, the high current will melt the fuse and create an open circuit to stop the current flow.
6. b: The thinner the wire, the higher the resistance. When the current is high, the wire used must be thick to ensure that there is no overheating along the wire which may lead to an outbreak of fire. For an operating current of 2.0 A, the thinnest wire which is available from the list is 0.15mm diameter wire which can safely carry a maximum current of 2.3 A.
7. c: It operating current of the appliance can be calculated by I = P/V. The operating current for this case = 750/240 = 3.125 A. The smallest diameter wire which can be safely used for this kettle is 0.20mm. This wire can safely carry a maximum current of 4.0 A.
Structured Questions and Solutions
Q1. An electrical fan labelled as '250 V, 50 W' is operated for 10 hours.
a. What is the operating current of the electrical fan?
b. Calculate the energy dissipated by the fan in kWh.
c. Calculate the cost of using the fan given that each unit of electricity costs $0.30.
a. P = IV
50 = 250 x I
I = 0.2 A
b. P = 50 W = 0.05 kW
E = Pt = 0.05 kW x 10 h = 0.5 kWh
c. 1 kWh costs $0.30.
0.5 kWh = $0.30 x 0.5 = $0.15
Q2. The diagram below shows a hair dryer, washing machine and heater connected to a 250 V mains. The hair dryer has a 1000 Ω resistance. The washing machine draws a current of 0.15 A. The heater has a rating of '250 V, 100 W'.
a. Calculate the normal working current of the hair dryer.
b. Calculate the electrical resistance of the washing machine.
c. Calculate the normal working current of the heater.
di. Indicate the position of the fuse of the hair dryer on the diagram.
dii. Given that the available fuses are 1 A, 2 A, 5 A, 13 A, and 15 A, which is suitable to replace fuse X?
e. Given that the cost of 1 unit of electricity is $0.20, calculate the cost of switching on the heater for 30 min.
f. Calculate the power of the heater should it be connected to a 120 V supply.
a. Current = V/R = 250/1000 = 0.25 A
b. R = V/I = 250/0.15 = 1670 Ω
c. I = P/V = 100/250 = 0.4 A
dii. Total current through the mains live wire = 0.25 + 0.15 + 0.4 = 0.8 A
Suitable fuse rating = 1 A
e. Power of heater = 0.1 kW
Energy = Pt = 0.1 x 0.5 = 0.05 kWh
Cost = 0.05 x $0.20 = $0.01
f. Resistance of heater = V/I = 250/0.4 = 625 Ω
Power of heater when placed across 120 V = V2/R = 1202 / 625 = 23.04 W
Q3. The table lamp shown below is made from plastic. It has only two wires in the cable. The lamp has a power rating of 100W and is used on a 230V supply.
ai. State which wire, earth, live or neutral, is not needed in the cable for the table lamp.
aii. Explain why the lamp is safe to use even though it has only two wires.
bi. Explain what is meant by a power rating of 100W.
bii. Calculate the value of the fuse that should be used in the plug for this table lamp.
biii. Calculate the electrical energy supplied to the lamp in 30 min.
ai. earth wire
aii. The lamp is made of plastic, which is a bad conductor of electricity.
bi. The energy liberated is at the rate of 100 J/s
bii. current = (100/230) A
value of fuse = 0.5 A
biii. energy = power x time
= 100 x 30 x 60
= 180 000 J
4. An appliance is connected to the live, neutral and earth conductors of the mains supply. The current in the circuit is 4.0A and the rating of the fuse is 5A.
a. Explain what is meant by
b. When a fault occurs in the appliance, no damage or injury is caused provided that the correct fuse is used and the metal case is connected to earth.
i. The 5A fuse is replaced by a 30A fuse. Explain why this presents a risk of damage or injury.
ii. The earth is not connected to the metal case. Explain why this presents a risk of damage or injury.
c. State one advantage of using a circuit breaker rather than a fuse to protect the appliance.
d. Describe an experiment to check that a fuse blows at 5A. In your account, draw a diagram of the apparatus and describe the procedures.
ai. The wire which is kept at high potential.
aii. The wire which is kept at 0 V.
bi. The current 30A is much greater than the circuit current 4A. The 30A fuse does not melt, and break the circuit, until current rises above 30A. This high current is a cause of damage or injury.
bii. If the live wire, due to damage, comes into contact with the metal case, it becomes live. When the user touches the metal case an electrical shock is received.
c. The circuit breaker can be reset, while the fuse wire has to be changed.
Adjust the rheostat setting to maximum resistance and then close the circuit.
The current is negligible.
Slowly change the rheostat setting to decrease the resistance.
The current in the circuit increases.
When the current reaches 5A, the fuse blows, breaking the circuit.