An electric element is enclosed in a copper or nickel tube, and electrically insu- lated from it with a mineral insulation of magnesium oxide. The resulting heater is immersed in the water to be heated. Heat is transferred to the water by conduction, after which the water circulates naturally by a process of convection. There are many types of electric water heater, one of the most common being shown in Figure 5.7.
Other heating applications
There are very many more applications of electric heating in industry, in commerce and at home. For example, welding is widely used for fabrication, and electric furnaces are used to produce steel and other alloys.
In the home, the electric cooker, kettle, iron and radiator are electric heaters that are often taken for granted.
5.4 Summary of formulas for Chapter 5
P = W
t = IU = I2R = U2
R
where P = power dissipated, W; W = energy expanded, J; t = time taken, s; I = circuit current, A; R = circuit resistance, ; and U = circuit potential difference, V.
Note that P = IU and P = U2/R are not always true for AC circuits.
Electrical power and energy 103
5.5 Exercises
1 An electric fire takes a current of 6.25 A from a 230 V supply. What power does it dissipate?
2 How much power will be dissipated in a 3 resistor when it is connected across a 12 V battery?
3 A coil of resistance 5 carries a current of 10 A. What power is dissipated in the coil?
4 A hall is lit by 20 lamps, each of which takes 0.5 A when connected to a 230 V supply. Calculate the total power supply to the lamps.
5 What is the resistance of an electric-fire element rated at 1 kW when carrying a current of 5 A?
6 When it is dissipating a power of 1 W, the PD across a carbon radio resistor is 100 V. What is the resistance?
7 What current will a 750 W fire element take from a 230 V supply?
8 How much current will a 10 resistor be carrying if the power lost in the resistor is 1 kW?
9 A 3 kW heating element has a resistance of 30 . For what supply voltage was the heater designed?
10 A 10 k resistor in an electronic circuit has 0.5 W of power lost in it. What current is it carrying and what is the PD across it?
11 How much energy will be consumed by the resistor in Exercise 10 in 10 min? 12 An electric water heater must provide 4 MJ of energy to heat its contents in
50 min. What is the power rating of the heating element?
13 An underfloor heating system has a loading of 20 kW. How much energy will it consume in 10 h?
14 A 10 resistor carries a current of 5 A. How much energy will it dissipate as heat each minute?
15 A 2 resistor liberates as heat 1440 J of energy in 20 s. What is the PD across the resistor?
16 A motor with an output of 8 kW and an efficiency of 80% runs for 8 h. Calculate the cost if electricity costs 6 pence per unit.
17 A generator in a motor car charges the battery at 20 A at 16 V. The generator efficiency is 43%. What power is absorbed in driving it?
18 The rating of the hotplate of an electric cooker is unknown. At 6 pm the meter reads 14 567 units. The cooker hotplate is at once switched on, together with a 1 kW fire and 500 W of lighting, and left on until 10 pm, when the meter reads 14 581 units. What is the rating of the hotplate?
19 It costs 40 pence to run a motor for 2 h, the tariff being 6.67 pence per unit. If the motor is 90% efficient, what is its output?
20 An electric water heater provides 4.8 MJ in 40 min. What is the rating of the element and how much current does it take from a 230 V supply?
21 A workshop supplied at 250 V has two motor drives at 1 kW each, a fan which takes 1 A, two 100 W lamps, a 2 kW radiator and a battery charger which takes
50 W. Calculate the total load in kilowatts and the weekly cost at 6 pence per unit if the load is on for 40 h a week.
22 A resistor of unknown value is connected in series with two 4 resistors, which are connected in parallel, across a 30 V supply. The power dissipated in each 4 resistor is 16 W. Calculate the value of the unknown resistor.
23 Resistors of 5 , 10 and 30 are connected in parallel. The combination is connected in series with a 7 resistor across a 50 V supply. Calculate the power dissipated in each resistor.
24 A 60 resistor and a resistor of unknown value are connected in series with each other and with a parallel combination of a 200 and a 50 resistor. This circuit is connected to a 240 V supply. If the power dissipated in the circuit is 480 W, what is the value of the unknown resistor?
25 An electric radiator has a resistance of 19 and is connected to a supply by a cable of resistance 1 . A second radiator of 38 resistance is connected to the supply by a cable of resistance 2 . The supply voltage is 230 V. Calculate (a) the current in each radiator and (b) the total power taken from the mains. 26 A domestic load comprises twelve 60 W lamps, eight 100 W lamps, two 2 kW
radiators and a 3 kW immersion heater. The lamps are fed from a lighting circuit and the power from a ring-main circuit. The supply is at 230 V. What is the current in each circuit? Suggest a suitable fuse for each circuit from ratings of 2 A, 5 A, 10 A, 13 A, 20 A and 30 A.
27 A small flat has the following loads: 3 × 100 W lamps in use 5 h each day 1 × 2 kW heater in use 4 h each day
1 × 3 kW immersion heater in use 3 h each day 1 × 4 kW cooker in use 2 h each day
The tariff for the supply of electricity is a fixed charge of 18 pence per week, plus an energy charge of 5 pence per unit. Find the total electricity cost for one week. 28 A water heater is 83.7% efficient and is required to heat 12 litres of water from 15◦C to 75◦C in 1 h. What minimum rating is required for the element? The
specific heat of water is 4187 J/kg K.
29 How long will a 3 kW heater take to raise the temperature of 30 litres of water from 20◦C to 90◦C if 10% of the heat supplied is lost in the process? The
specific heat of water is 4187 J/kg K.
30 A builder’s hoist lifts 100 kg of bricks through 40 m in 20 s. If the hoist is 75% efficient, what is the rating of the electric motor driving it?
31 If the motor of the previous exercise is fed from a 200 V DC supply and is 80% efficient, calculate its running current.
32 A lift motor takes a current of 20 A from a 300 V DC supply. The lift gearing is 50% efficient. If the lift is able to raise a load of 1440 N through a height of 50 m in 30 s, what is the efficiency of the motor?
33 Calculate the output of a motor with an input of 24 kW and an efficiency of 90%. 34 A motor with an output of 10 kW and an efficiency of 85% drives a drilling machine which is 60% efficient. What is the output of the machine, and what is the input of the motor?
Electrical power and energy 105
5.6 Multiple-choice exercises
5M1 The unit of electrical power is the(a) volt (b) ampere
(c) watt (d) horsepower
5M2 The power dissipated in an 800 resistor connected to a 230 V supply is (a) 66.1 W (b) 0.3 A
(c) 7.2 W (d) 192 W
5M3 An electric lamp is rated at 60 W. The current it draws from a 230 V supply is
(a) 4 A (b) 14.4 A
(c) 6.94 µA (d) 0.261 A
5M4 If the 60 W lamp of question 5M3 is left on for 8 h and electrical energy costs 7 pence per unit, the cost will be
(a) 3.36 p (b) £3.36
(c) 5.25 p (d) 6.86 p
5M5 The energy used by the 60 W lamp of exercise 5M4 in 8 h is (a) 480 J (b) 172.8 kJ
(c) 28.8 kJ (d) 60 W
5M6 A resistor of value 33 is connected to a 100 V supply through a cable with a total resistance of 0.3 . The thermal energy in the cable is
(a) 300 W (b) 3.63 W
(c) 2.71 W (d) 33.3 kW
5M7 Resistors are connected in a series–parallel group as shown in the figure below. The power dissipated in the 5 resistor is
(a) 2.56 W (b) 45 W (c) 80 W (d) 4 A 6 Ω 6 Ω 1·25 Ω 5 Ω 20 V
5M8 The SI unit of force is the
(a) pound (b) horsepower
(c) joule (d) newton
5M9 The number of newtons in one kilogram is
(a) 9.81 (b) 33 000
(c) 453.6 (d) 3 600 000
5M10 If 120 J of energy is used to move a force of 10 N, the distance moved is
(a) 1.2 m (b) 12 m
5M11 A block-and-tackle system is 40% efficient and lifts a load of 300 kg to a height of 4 m in 10 s. The input power required is
(a) 3 kW (b) 4.70 kW
(c) 2.94 kW (d) 480 W
5M12 The operation of a filament lamp depends on
(a) the fact that certain powders emit light (fluoresce) when stimulated (b) the filament being heated to a temperature that causes it to glow and
emit visible light (c) a gas jet being lit
(d) a bayonet-cap lampholder
5M13 The water is an electric water heater is warmed from the element by the process of
(a) convection (b) radiation
(c) a copper or nickel tube (d) conduction
5M14 A fan-type thermal-storage heater is less expensive to run than a direct electric heater because
(a) it has a fan which circulates air through it (b) it is usually provided with input and fan controls
(c) it is charged with cheaper electrical energy at offpeak times (d) it has very efficient thermal insulation