Energy and work
1.13 Summary of formulas for Chapter
Q = It I = Qt t = QI
where Q = electric charge, C; I = current, A; and t = duration of current, s.
W = dF d = WF F = Wd
where W = energy used or work done, mN or J; F = force applied, N; and
d = distance moved, m. P = W
t W = Pt t = W
P
where P = power or rate of doing work, W.
W = UQ Q = W U U =
W Q
where U = potential difference, V. For resistors in series:
R = R1+ R2+ R3· · ·
For resistors in parallel: 1 R = 1 R1+ 1 R2 + 1 R3+ · · ·
where R = total circuit resistance, ; R1, R2, R3 etc. = individual circuit resis-
tances, .
I = U R R =
U
I U = IR
1.14 Exercises
1 A current of 10 A flows for 2 min. What charge is transferred?
2 For how long must a current of 4 mA flow so as to transfer a charge of 24 C? 3 What current must flow if 100 C is to be transferred in 8 s?
4 Briefly describe one example of each of the chemical, heating and electromag- netic effects of an electric current.
5 A force of 450 N is required to lift a bundle of conduit. How much work is done if it raised from the floor to the roof rack of a van 2 m high?
6 Energy of 2 J is required to close a contactor against a spring exerting a force of 80 N. How far does the contactor move?
7 When an electric motor is pushed 30 m across a level floor, 4500 J of work is done. What force is needed to move the motor?
8 A force of 35 N is required at the end of a spanner 0.2 m long to move a nut on a thread. How much work is done in giving the nut one complete turn? 9 A DC generator has an EMF of 200 V and provides a current of 10 A. How much
energy does it provide each minute?
10 A photocell causes a current of 4 µA in its associated circuit, and would take 1000 days to dissipate an energy of 1 mJ. What EMF does it provide?
11 An electric blanket is required to provide heat energy at the rate of 7200 J/min from a 230 V supply. What current will flow?
12 If the total resistance of an earth fault loop is 4 , what current will flow in the event of a phase-to-earth fault from 230 V mains?
13 During a flash test, a voltage of 20 kV is applied to a cable with an insulation resistance of 5 M. What will be the leakage current?
14 What is the resistance of an immersion-heater element that takes 12.0 A from a 230 V supply?
15 An indicator lamp has a hot resistance of 50 and a rated current of 0.2 A. What is its rated voltage?
16 The PD across an earth-continuity conductor of resistance 0.3 is found to be 4.5 V. What current is the conductor carrying?
17 Four resistors of values 5, 15, 20 and 40 , respectively, are connected in series to a 230 V supply. Calculate the resulting current and the PD across each resistor.
18 A 6 resistor and a resistor of unknown value are connected in series to a 12 V supply, when the PD across the 6 resistor is measured as 9 V. What is the value of the unknown resistor?
19 Calculate the resistance of the element of a soldering iron that takes 0.5 A from 230 V mains when connected to them by cables having a total resistance of 0.2 . 20 Calculate the equivalent resistance of each of the following parallel-connected
resistor banks: (a) 2 and 6
(b) 12 M, 6 M and 36 M; and (c) 100 µ, 600 µ and 0.0012
Basic electrical units and circuits 29 21 Answer the following questions by writing down the missing word or words:
(a) A fuse protects a circuit against …… and uses the …… effect of an electric current.
(b) The unit of quantity of electricity is called the …….
(c) Two good conductors of electrical current are …… and …….
(d) Two items of electrical equipment that use the electromagnetic effect are …… and …….
(e) Two insulating materials used in the electrical industry are …… and ……. (f) In an electrical circuit, the electron flow is from the …… terminal to the
…… terminal.
(g) A bimetallic strip uses the …… effect of an electric current. (h) The electron has a …… charge.
(i) An EMF of 72 V is applied to a circuit, and a current of 12 A flows. The resistance of the circuit is …….
(j) The effective resistance of two 10 resistors connected in parallel is ……. (k) Quantity of electricity = …… × …….
(l) 0.36 amperes = …… milliamperes. (m) 3.3 kilovolts = …… volts.
22 Three resistors are connected in parallel across a supply of unknown voltage. Resistor A is of 7.5 and carries a current of 4 A. Resistor B is of 10 , and resistor C is of unknown value but carries a current of 10 A. Calculate the supply voltage, the current in resistor B and the value of resistor C.
23 Three parallel-connected busbars have resistances of 0.1, 0.3 and 0.6 , respec- tively, and in the event of a short circuit, would be connected directly across a 400 V supply. Calculate the equivalent resistance of the combination, the total fault current and the current in each busbar.
24 Resistors of 7, 14 and 14 , respectively, are connected in parallel. This bank is connected in series with a 2.5 resistor across a supply of unknown PD. The current flow in the 2.5 resistor is 2 A. What is the supply voltage?
25 (a) Show, by separate drawings for ‘high’, ‘medium’ and ‘low’ heat positions, the connections of a series–parallel switch controlling two separate sections of resistance wire forming the elements of a heating appliance.
(b) If the two sections of resistance wire are of equal resistance, what is the proportional current flow and heating effect in the ‘medium’ and ‘low’ positions relative to the ‘high’ position.
26 Three resistors, having resistances of 4.8 , 8 and 12 , all connected in parallel, are supplied from a 48 V supply. Calculate the current through each resistor and the current taken from the supply. Calculate the effective resistance of the group.
27 Two resistances of 4 and 12 are connected in parallel with each other. A further resistance of 10 is connected in series with the combination. Calculate the respective direct voltages which should be applied across the whole circuit (a) to pass 6 A through the 10 resistance
28 (a) State Ohm’s law in words and with symbols.
(b) Three relay coils, each of 7.5 resistance, are connected in parallel. What current would flow in the circuit when the supply is 12 V?
(c) Calculate the resistance required to limit the current in a circuit to 4.8 A with a voltage of 200 V.
29 Three banks of resistors are connected in series across a 240 V supply. Bank A consists of three resistors R1, R2and R3, each of resistance 60 , connected
in parallel. Bank B comprises two resistors, R4of resistance 40 and R5of
resistance 120 , connected in parallel. Bank C has three parallel-connected resistors, R6= 50 , R7= 100 and R8= 300 . Calculate
(a) the resistance of the complete circuit (b) the current in each resistor
(c) the PD across each resistor
30 A resistance network is connected as shown in Figure 1.16, and takes a total current of 2.4 A from the 24 V supply. Calculate the value of the resistor Rx. 31 The voltmeter shown in Figure 1.17 reads 39 V. What is the value of the resistor
across which the voltmeter is connected?
7 Ω 4 Ω 12 Ω 1.6 Ω 2·4 A 24 V Rx
Figure 1.16 Circuit diagram for Exercise 1.30
14 Ω 6 Ω 24 Ω 12 Ω V 100 V
Figure 1.17 Circuit diagram for Exercise 1.31
32 Three banks of resistors are connected in series. Bank 1 consists of 40 and 24 in parallel; bank 2 comprises a single resistor of 5 ; bank 3 comprises four resistors in parallel, each of 16 . Ammeters are inserted to measure the current through each resistor, and voltmeters to measure the voltage across each bank.
Basic electrical units and circuits 31 Sketch a layout of the apparatus, and calculate the reading on each instrument if 48 V is applied to the circuit.
33 A bank of three paralleled resistors each of 12 is connected in series with another bank consisting of three resistors in parallel, their values being 4 , 4 , and 2 . If a 100 V supply is applied across this circuit, what current would flow through the 2 resistor?