Donat Sciences and Maths
Senior 3 practice book · Unit 6 of 10

Basic Electrical Wiring and Installation

50 questions that complete the Senior 3 quiz for this unit: 27 core and 23 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions
  • Current is used up by each lamp, so less current returns to the supply than leaves it.Charge flows round the circuit without being used up: the current into a lamp equals the current out. The lamp takes energy from the charges, not the charges themselves.
  • Switching on more appliances in a house increases the total resistance of the house circuit.Appliances are in parallel, so every extra branch is another path for charge: the total resistance falls and the current in the main cable rises.
  • The earth wire carries the current that makes an appliance work.The live and neutral wires carry the working current. The earth wire carries current only during a fault, and that large current makes the fuse or breaker cut the supply.
  • A battery marked 12 V always gives 12 V across its terminals.12 V is the e.m.f. When current flows, some voltage (Ir) is lost inside the battery, so the terminal voltage is less than 12 V and falls further as the current grows.
  • A switch in the 'off' position makes a lamp holder completely safe to touch.If the switch is wrongly placed in the neutral wire, the holder is still joined to live when the lamp is off. Always isolate the circuit at the distribution board and test it before touching.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

  • Series and parallel combinations of resistors
  • E.m.f., internal resistance and terminal voltage of a cell
  • Main parts of a house installation: service entrance, energy meter, distribution board, switches and sockets
  • Protective devices: fuses, MCBs and RCDs, and choosing a rating
  • Earthing, bonding and double insulation
  • Stages of the installation process: planning, conduits, termination, mounting, testing, energizing, handover
  • Electrical power, energy in kWh and the cost of electricity
  • Three-core cable, colour codes and the three-pin plug
  • Lighting and socket circuits: one-way and two-way switching, radial and ring circuits
  • Measuring and testing: ammeter, voltmeter, multimeter, continuity and insulation tests
  • Electrical hazards, safe working and first aid for electric shock
  • Wiring tools and materials: strippers, testers, conductor material and cable size
Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 23 harder ones are marked ★ Challenge.

  1. 1True or false

    In a correctly wired three-pin plug, the fuse is connected to the live (brown) wire.

    Show answer
    Answer: True

    The fuse must be in the live side so that when it melts the appliance is cut off from the high voltage.

    Common mistakeSome learners think the fuse can be in any wire; in the neutral it would leave the appliance connected to live after blowing.
  2. 2True or false · ★ Challenge

    It is safe to change a broken lamp holder as long as the wall switch for that lamp is turned off.

    Show answer
    Answer: False

    The switch may have been wired in the neutral, or another circuit may feed the holder. Switch off the circuit at the distribution board and test that it is dead first.

    Common mistakeLearners trust the wall switch; it is not a safe isolation point because it may not break the live wire.
  3. 3True or false

    The main switch on the distribution board allows the whole house to be disconnected from the supply for repairs.

    Show answer
    Answer: True

    Turning off the main switch isolates every final circuit at once, which is the safe first step before any electrical work.

    Common mistakeSome think each breaker must be switched off one by one; the main switch cuts every circuit together.
  4. 4Multiple choice · ★ Challenge

    By mistake, a learner connects an ammeter in parallel with a lamp in a working circuit. What is most likely to happen?

    1. AThe lamp glows brighter and the ammeter shows its true current
    2. BNothing changes, but the ammeter reads zero
    3. CThe lamp goes out and a large current may damage the ammeter
    4. DThe lamp stays lit and the ammeter reads the voltage
    Show answer
    Answer: C. The lamp goes out and a large current may damage the ammeter

    An ammeter has a very low resistance, so it short-circuits the lamp: almost all the current goes through the meter, the lamp goes out and the meter's fuse may blow.

    Common mistakeChoosing 'nothing changes' forgets that the ammeter's tiny resistance offers an easy path that takes current away from the lamp.
  5. 5True or false

    The combined resistance of resistors in parallel is always smaller than the smallest single resistor in the group.

    Show answer
    Answer: True

    Each parallel branch adds an extra path for charge, so the combination conducts better than any one branch alone.

    Common mistakeMany learners think parallel resistance is an average of the values, but it is always below the smallest one.
  6. 6Multiple choice · ★ Challenge

    In a ring circuit, the cable leaves the distribution board, passes every socket and returns to the board. What is the main advantage?

    1. AIt makes every socket receive twice the normal mains voltage
    2. BIt means no fuse or breaker is needed for the socket outlets
    3. CIt lets the earth wire be left out of the cable completely
    4. DCurrent reaches each socket by two paths, so thinner cable will do
    Show answer
    Answer: D. Current reaches each socket by two paths, so thinner cable will do

    Because the current shares two routes, each part of the ring carries roughly half the current, so the cable heats less.

    Common mistakeChoosing 'twice the voltage' is wrong: every socket is still connected between live and neutral at 230 V; only the current paths change.
  7. 7True or false

    In a radial socket circuit, one cable runs from the distribution board to each socket in turn and ends at the last socket.

    Show answer
    Answer: True

    A radial circuit is a single line that does not return to the board, unlike a ring circuit.

    Common mistakeLearners often mix up radial and ring circuits; only a ring circuit returns to the board.
  8. 8Short answer · ★ Challenge

    List three precautions an electrician should take before working on a lighting circuit in a school.

    Show answer
    Model answer: Any three: switch off the circuit (or the main switch) at the distribution board; lock it off or put up a warning notice so nobody switches it on again; test with a tester or meter that the circuit is really dead; use tools with insulated handles; stand on a dry surface and wear dry shoes.
    Common mistakeMany learners stop at 'switch it off'; the circuit must also be tested dead and protected against someone switching it back on.
  9. 9True or false

    Joints in house cables should be made at proper terminals or inside junction boxes, not by twisting bare wires together and hiding them in the plaster.

    Show answer
    Answer: True

    Twisted joints become loose, heat up and can start a fire; joints in boxes can also be inspected and repaired.

    Common mistakeLearners think a twisted joint is fine if it is taped; loose joints have high resistance and overheat over time.
  10. 10Multiple choice · ★ Challenge

    Which of these uses the MOST electrical energy?

    1. AA 100 W television on for 4 h
    2. BA 2000 W kettle on for 6 minutes
    3. CA 10 W LED lamp on for 24 h
    4. DA 1000 W iron on for 15 minutes
    Show answer
    Answer: A. A 100 W television on for 4 h

    E = Pt: TV 0.1 kW × 4 h = 0.40 kWh; kettle 2.0 × 0.1 = 0.20 kWh; LED 0.010 × 24 = 0.24 kWh; iron 1.0 × 0.25 = 0.25 kWh.

    Common mistakeChoosing the kettle confuses power with energy; a high-power appliance used briefly can use less energy than a low-power one used for hours.
  11. 11Fill in the blank

    In a three-core cable, the wire with green-and-yellow striped insulation is the ______ wire.

    Show answer
    Answer: earth

    Green-and-yellow is always the earth (protective) conductor; brown is live and blue is neutral.

    Common mistakeSome learners think green-and-yellow is neutral because it carries no current in normal use; neutral is blue.
  12. 12True or false · ★ Challenge

    A person touching a live wire may be killed by a current of about 50 mA, far below the 13 A that would blow a plug fuse, which is why an RCD that trips at 30 mA gives extra protection.

    Show answer
    Answer: True

    Fuses and MCBs protect cables against large currents; only an RCD reacts to the small earth-leakage currents that pass through a body.

    Common mistakeMany think a fuse protects people from shock; a fuse rated in amps does nothing about a current of a few tens of milliamps through a person.
  13. 13Fill in the blank

    A hair dryer with an all-plastic case, marked with a square inside a square, is called double ______ and does not need an earth wire.

    Show answer
    Answer: insulated

    Two separate layers of insulation mean no metal part a user can touch could become live, so an earth wire is not needed.

    Common mistakeLearners often think every appliance needs an earth wire; only appliances with touchable metal parts must be earthed.
  14. 14Fill in the blank

    A switch that can connect its common terminal to either of two other terminals, used for staircase lighting, is called a two-______ switch.

    Show answer
    Answer: way

    A two-way switch directs the current along one of two strapping wires.

    Common mistakeSome write 'two-pole', which is a switch that breaks two wires at once; that is a different device.
  15. 15Multiple choice · ★ Challenge

    A 20 A MCB protects a workshop socket circuit on a 230 V supply. Which pair of appliances, used together, will make it trip?

    1. AA 2400 W kettle and a 2000 W heater
    2. BTwo 2200 W room heaters
    3. CA 3000 W oven and a 2000 W kettle
    4. DA 3000 W oven and a 1500 W iron
    Show answer
    Answer: C. A 3000 W oven and a 2000 W kettle

    I = P ÷ V: 5000 ÷ 230 = 21.7 A, more than 20 A. The others give 4400 ÷ 230 = 19.1 A (twice) and 4500 ÷ 230 = 19.6 A.

    Common mistakeChoosing the oven and iron (19.6 A) is tempting because it contains the biggest appliance; only the total current matters, and 4500 W is still just under 20 A.
  16. 16Multiple choice

    To measure the current through a lamp, an ammeter must be connected:

    1. AIn parallel with the lamp, across its two terminals
    2. BIn series with the lamp, so the same current flows through it
    3. CBetween the lamp and the earth wire of the circuit
    4. DAcross the battery terminals, in parallel with the whole supply
    Show answer
    Answer: B. In series with the lamp, so the same current flows through it

    An ammeter measures the current flowing through it, so the same current as the lamp's must pass through the meter: it goes in series.

    Common mistakeChoosing 'in parallel' mixes up the ammeter with the voltmeter, which is connected across a component.
  17. 17Short answer · ★ Challenge

    Copper and aluminium both conduct electricity. Suggest two reasons why copper is preferred for the cables inside houses.

    Show answer
    Model answer: Copper has a lower resistivity, so a copper cable of the same size has less resistance and heats less. Copper is also stronger and more flexible, so it can be bent round corners without breaking, and its connections at terminals stay tight and do not corrode as easily.
    Common mistakeSome learners say copper is chosen because it is cheaper; aluminium is actually cheaper and lighter, which is why it is used on overhead lines.
  18. 18Multiple choice

    A residual current device (RCD) detects an earth fault by comparing the currents in which two wires?

    1. AThe live wire and the earth wire
    2. BThe neutral wire and the earth wire
    3. CThe live wire and the neutral wire
    4. DThe earth wire and the water pipe
    Show answer
    Answer: C. The live wire and the neutral wire

    Normally the current out along live equals the current back along neutral. If some current leaks to earth (perhaps through a person), they differ and the RCD trips.

    Common mistakeChoosing live and earth is tempting because the leak goes to earth, but the RCD senses it as a difference between live and neutral currents.
  19. 19Short answer · ★ Challenge

    A learner wires a plug for a kettle but swaps the brown and blue wires. The kettle still boils water. Explain why this mistake is dangerous.

    Show answer
    Model answer: The kettle's own switch is designed to break the live side, but now it is in the wire connected to neutral. When the kettle is switched off, its element and internal parts are still connected to the live supply, so someone cleaning or repairing it could get a shock.
    Common mistakeLearners often think 'if it works, it is wired correctly'; current flows either way, but the switch and protection end up on the wrong side.
  20. 20Fill in the blank

    The voltage used up inside a cell to drive current through its own internal resistance, equal to I × r, is often called the 'lost ______'.

    Show answer
    Answer: volts

    Lost volts = Ir; the terminal voltage is the e.m.f. minus the lost volts.

    Common mistakeSome learners think the lost volts are lost in the connecting wires; they are lost inside the cell itself.
  21. 21Multiple choice · ★ Challenge

    A prepaid energy meter in a Huye home shows 152.4 units left on Monday morning and 138.9 units left on Thursday morning. What is the average energy used per day?

    1. A4.5 kWh
    2. B13.5 kWh
    3. C3.4 kWh
    4. D46 kWh
    Show answer
    Answer: A. 4.5 kWh

    Energy used = 152.4 − 138.9 = 13.5 kWh over 3 days (Monday to Thursday morning), so 13.5 ÷ 3 = 4.5 kWh per day. One unit = 1 kWh.

    Common mistakeChoosing 3.4 kWh counts four days (Monday, Tuesday, Wednesday, Thursday); from Monday morning to Thursday morning is only three full days.
  22. 22Multiple choice

    Which tool is designed to remove the insulation from the end of a cable without cutting the copper inside?

    1. AA hacksaw
    2. BA tester screwdriver
    3. CA claw hammer
    4. DA wire stripper
    Show answer
    Answer: D. A wire stripper

    A wire stripper has adjustable notches that cut only through the plastic insulation.

    Common mistakeChoosing a hacksaw is wrong: it cuts through everything, including the copper conductor that is needed.
  23. 23Short answer · ★ Challenge

    A student wires a corridor lamp with two ordinary on/off switches in series, one at each end. Describe what goes wrong when a teacher tries to use it.

    Show answer
    Model answer: The lamp lights only when both switches are on. If the switch at the far end is off, the teacher cannot turn the lamp on from the near end; and if it is on, turning it off at one end leaves the other end unable to turn it on again. Two-way switches are needed.
    Common mistakeA common belief is that two switches always give control from two places; ordinary switches in series behave like an AND gate, not like staircase switching.
  24. 24Multiple choice

    A person is gripping a faulty cable and receiving an electric shock in a kitchen. What should you do first?

    1. ASwitch off at the main switch, or push them away with dry wood
    2. BPull the person away quickly with your bare hands
    3. CThrow a bucket of water over the person to cool them
    4. DWait for the fuse in the circuit to blow on its own
    Show answer
    Answer: A. Switch off at the main switch, or push them away with dry wood

    You must break the contact without becoming part of the circuit: cut the supply, or use a dry non-conducting object. Then give first aid and call for help.

    Common mistakePulling with bare hands is the most tempting choice but makes the rescuer part of the circuit, so both people can be electrocuted.
  25. 25Multiple choice

    The neon lamp in a tester screwdriver glows when its tip touches a terminal. This shows that the terminal is:

    1. ALive
    2. BNeutral
    3. CEarth
    4. DDead
    Show answer
    Answer: A. Live

    A tiny current flows from the live terminal through the neon lamp and your body to earth, making the neon glow.

    Common mistakeChoosing 'neutral' is a common mix-up: neutral is close to earth potential, so the neon stays dark.
  26. 26Short answer · ★ Challenge

    When a driver turns the key to start a car while the headlamps are on, the headlamps dim for a moment. Explain this using the idea of internal resistance.

    Show answer
    Model answer: The starter motor draws a very large current from the battery. The lost volts inside the battery, Ir, become large, so the terminal voltage V = E − Ir falls. The headlamps are connected across the terminals, so they get less voltage and glow dimmer until the motor stops.
    Common mistakeA common wrong answer is that the e.m.f. falls; the e.m.f. stays the same, it is the voltage lost inside the battery that grows with the current.
  27. 27Multiple choice

    Which arrangement lets a staircase light be switched on or off from both the bottom and the top of the stairs?

    1. ATwo one-way switches connected in series, one at each end
    2. BTwo one-way switches connected in parallel
    3. COne switch in live and one switch in neutral
    4. DTwo two-way switches joined by two strapping wires
    Show answer
    Answer: D. Two two-way switches joined by two strapping wires

    With two-way switches, changing either switch always changes the state of the lamp, whatever the position of the other.

    Common mistakeChoosing two one-way switches in series fails: the lamp then lights only when BOTH are on, so one person cannot control it alone.
  28. 28Multiple choice · ★ Challenge

    The resistance of a person's body is about 100 kΩ with dry skin and about 1 kΩ with wet skin. What current would flow through the body from a 230 V live wire in each case?

    1. A230 mA dry, 2.3 mA wet
    2. B2.3 mA dry, 230 mA wet
    3. C23 A dry, 0.23 A wet
    4. D2.3 mA in both cases
    Show answer
    Answer: B. 2.3 mA dry, 230 mA wet

    I = V ÷ R: dry 230 ÷ 100 000 = 0.0023 A = 2.3 mA; wet 230 ÷ 1000 = 0.23 A = 230 mA, which can stop the heart.

    Common mistakeChoosing '230 mA dry, 2.3 mA wet' reverses the effect: the smaller the resistance, the larger the current.
  29. 29Multiple choice

    An insulation tester measures the resistance between the live and earth conductors of a newly wired circuit. Which reading is the most satisfactory?

    1. AAbout 0.2 Ω
    2. BAbout 50 Ω
    3. CBetween 2 kΩ and 5 kΩ
    4. DMore than 200 MΩ
    Show answer
    Answer: D. More than 200 MΩ

    Good insulation lets almost no current leak between conductors, so its resistance must be very high (at least about 1 MΩ). A low reading means damaged insulation or a short circuit.

    Common mistakeChoosing 0.2 Ω confuses this with a continuity test, where a low reading is good; for insulation a HIGH resistance is good.
  30. 30Multiple choice · ★ Challenge

    A fault joins the live wire (230 V) to the earthed metal case of a cooker. The fault path through the case and earth wire has a total resistance of 0.50 Ω. What happens?

    1. AAbout 460 A flows and the 13 A fuse blows at once
    2. BAbout 0.0022 A flows, so the 13 A fuse does not blow
    3. CAbout 115 A flows, but the 13 A fuse does not blow
    4. DExactly 13 A flows, the most that the fuse allows
    Show answer
    Answer: A. About 460 A flows and the 13 A fuse blows at once

    I = V ÷ R = 230 ÷ 0.50 = 460 A. This is far above 13 A, so the fuse melts almost instantly and the case is no longer live.

    Common mistakeChoosing 0.0022 A comes from dividing R by V (0.50 ÷ 230); Ohm's law gives I = V ÷ R, which is a very large current here.
  31. 31Fill in the blank

    One kilowatt-hour (1 kWh), the 'unit' on an electricity bill, is equal to ______ joules.

    Show answer
    Answer: 3.6 × 10⁶ (3 600 000)

    1 kWh = 1000 W × 3600 s = 3 600 000 J.

    Common mistakeSome learners write 1000 J or 3600 J, forgetting to multiply both the 1000 W and the 3600 seconds in one hour.
  32. 32Multiple choice · ★ Challenge

    Two lamps X and Y are in parallel across a 6.0 V battery. The ammeter in the main line reads 0.90 A and the ammeter in lamp X's branch reads 0.30 A. What is the resistance of lamp Y?

    1. A20 Ω
    2. B6.7 Ω
    3. C10 Ω
    4. D5.0 Ω
    Show answer
    Answer: C. 10 Ω

    Current in Y = 0.90 − 0.30 = 0.60 A, and Y has the full 6.0 V across it, so R = V ÷ I = 6.0 ÷ 0.60 = 10 Ω.

    Common mistakeChoosing 20 Ω uses lamp X's current (6.0 ÷ 0.30); in a parallel circuit the branch currents add up to the main current, so Y takes the difference.
  33. 33Fill in the blank

    House cables are sized by the cross-sectional ______ of their copper conductor, for example 1.5 mm² for lighting and 2.5 mm² for sockets.

    Show answer
    Answer: area

    A larger cross-sectional area gives a lower resistance, so the cable can carry more current without overheating.

    Common mistakeLearners sometimes think the size is the length of the cable; it is the area of the conductor's cross-section, in mm².
  34. 34Multiple choice

    An old house in Kigali has wiring with red, black and green insulation. A new extension uses brown, blue and green-and-yellow. Which old wire does the same job as the new brown wire?

    1. AThe black wire
    2. BThe green wire
    3. CThe red wire
    4. DNone of them
    Show answer
    Answer: C. The red wire

    In the old colour code red was live, black neutral and green earth; in the new code brown is live, blue neutral and green-and-yellow earth.

    Common mistakeChoosing black is tempting because black and brown are both dark colours, but black was the old neutral; brown is the live wire.
  35. 35Short answer · ★ Challenge

    Before starting work on a new house in Rwamagana, an electrician draws a wiring plan of every room. Suggest three ways this plan helps the job and the owner.

    Show answer
    Model answer: Any three: it shows where each lamp, switch and socket will go; it lets the electrician work out the lengths of cable and conduit and the number of accessories, and so estimate the cost; it groups the points into separate circuits so that none is overloaded; it becomes part of the documentation given to the owner for later repairs.
    Common mistakeSome learners think planning is only paperwork; a good plan prevents overloaded circuits and wasted materials, and saves time during later repairs.
  36. 36Multiple choice

    Why is the earth pin of a three-pin plug longer than the live and neutral pins?

    1. AIt carries more current than the others
    2. BIt connects first and disconnects last
    3. CIt holds the fuse inside it
    4. DIt stops the plug from overheating
    Show answer
    Answer: B. It connects first and disconnects last

    The long earth pin makes the earth connection before live is joined and keeps it until live is broken; it also opens the shutters on the live and neutral holes of the socket.

    Common mistakeChoosing 'carries more current' is wrong because the earth pin carries no current unless there is a fault.
  37. 37Short answer · ★ Challenge

    An electrician tests the insulation of four new circuits and records: lighting 300 MΩ, sockets 150 MΩ, cooker 0.4 MΩ, water heater 80 MΩ. The minimum acceptable value is 1 MΩ. Which circuit must be checked before the supply is switched on, and why?

    Show answer
    Model answer: The cooker circuit (0.4 MΩ is below 1 MΩ). Its insulation is poor, perhaps damaged by a nail or by water, so current could leak between conductors or to earth and cause a shock or fire. The fault must be found and repaired and the circuit retested.
    Common mistakeLearners sometimes pick the lighting circuit because 300 MΩ is the 'largest'; for insulation a large resistance is good and only a value below the minimum is a problem.
  38. 38True or false

    A voltmeter should have a very high resistance so that it draws almost no current from the circuit it is connected across.

    Show answer
    Answer: True

    If a voltmeter took a large current it would change the very voltage it is measuring.

    Common mistakeSome learners think meters should all have low resistance; that is true only for ammeters.
  39. 39Short answer · ★ Challenge

    A shopkeeper replaces a blown 5 A fuse with a nail, saying 'a nail never blows, so the shop will never lose power'. Evaluate this idea.

    Show answer
    Model answer: It is very dangerous. A nail has a very high melting point and can carry a huge current, so in a fault or overload the current is not cut off. The cables overheat, the insulation melts and a fire or electric shock can result. The fault that blew the fuse should be found and a correct 5 A fuse fitted.
    Common mistakeLearners may think the fuse 'causes' the power cut; the fuse only reacts to a fault or overload, and removing it removes the protection, not the fault.
  40. 40Multiple choice

    A string of 20 identical festive lamps is joined in series and plugged into the 230 V mains. What is the voltage across each lamp?

    1. A11.5 V
    2. B230 V
    3. C4600 V
    4. D0.087 V
    Show answer
    Answer: A. 11.5 V

    In series the supply voltage is shared: 230 ÷ 20 = 11.5 V per identical lamp.

    Common mistakeChoosing 230 V treats the lamps as if they were in parallel; in series each lamp receives only a share of the supply voltage.
  41. 41Multiple choice · ★ Challenge

    A school replaces ten 60 W filament bulbs with ten 9 W LED bulbs that give the same light. The lamps are on 5 h a day. How much money is saved in 30 days at 200 RWF per kWh (assume this price)?

    1. A1530 RWF
    2. B15 300 RWF
    3. C18 000 RWF
    4. D510 RWF
    Show answer
    Answer: B. 15 300 RWF

    Power saved = 10 × (60 − 9) = 510 W = 0.51 kW. Energy saved = 0.51 × 5 × 30 = 76.5 kWh. Saving = 76.5 × 200 = 15 300 RWF.

    Common mistakeChoosing 1530 RWF forgets that there are ten bulbs; multiply the saving per bulb by the number of bulbs.
  42. 42Short answer

    Put these parts in the order in which electricity passes through them, from the street cable to a ceiling lamp: lamp circuit, energy meter, service entrance, distribution board. Give one job of the energy meter.

    Show answer
    Model answer: Service entrance → energy meter → distribution board → lamp circuit. The energy meter records the electrical energy used by the house in kWh (units), so that it can be paid for.
    Common mistakeLearners often put the distribution board before the meter; the meter must come first so that it measures all the energy used by every circuit.
  43. 43Multiple choice · ★ Challenge

    A 2300 W, 230 V heater is at the end of a twin cable 20 m long (40 m of copper in all, live and neutral). The copper has a resistance of 0.012 Ω per metre. About how much voltage is lost in the cable?

    1. A2.4 V
    2. B0.48 V
    3. C4.8 V
    4. D230 V
    Show answer
    Answer: C. 4.8 V

    I = P ÷ V = 2300 ÷ 230 = 10 A. Cable resistance = 40 × 0.012 = 0.48 Ω. Voltage lost = IR = 10 × 0.48 = 4.8 V.

    Common mistakeChoosing 2.4 V uses only 20 m of wire; the current goes out along live and back along neutral, so both lengths count.
  44. 44Multiple choice

    A 1.5 V cell with internal resistance 0.25 Ω is short-circuited by a thick copper wire of almost zero resistance. What current flows?

    1. A0.38 A
    2. B1.5 A
    3. C0.17 A
    4. D6.0 A
    Show answer
    Answer: D. 6.0 A

    Only the internal resistance limits the current: I = E ÷ r = 1.5 ÷ 0.25 = 6.0 A, which quickly heats and drains the cell.

    Common mistakeChoosing 0.38 A multiplies E by r; current is voltage divided by resistance, I = E ÷ r.
  45. 45Short answer

    Give two reasons why you should never touch a switch or socket with wet hands.

    Show answer
    Model answer: Water lowers the resistance of the skin, so a much larger current can flow through the body if any live part is touched. Water can also run into the switch or socket and create a conducting path from the live parts to your hand.
    Common mistakeLearners often think water itself is the danger only because it 'carries electricity'; the main point is that wet skin has a far lower resistance, so the current through the body is much larger.
  46. 46Multiple choice · ★ Challenge

    A graph of terminal voltage V (y-axis) against current I (x-axis) for a cell is a straight line. It starts at 1.6 V when I = 0 and falls to 1.0 V when I = 1.2 A. What are the e.m.f. E and internal resistance r?

    1. AE = 1.0 V, r = 0.83 Ω
    2. BE = 1.6 V, r = 0.50 Ω
    3. CE = 1.6 V, r = 2.0 Ω
    4. DE = 1.6 V, r = 1.3 Ω
    Show answer
    Answer: B. E = 1.6 V, r = 0.50 Ω

    E is the intercept on the V-axis, 1.6 V. r = −gradient = (1.6 − 1.0) ÷ 1.2 = 0.50 Ω.

    Common mistakeChoosing r = 2.0 Ω comes from dividing current by voltage (1.2 ÷ 0.6); the gradient is the voltage change divided by the current change.
  47. 47Short answer

    Describe how a multimeter set to its continuity (or lowest ohms) range can show whether a cartridge fuse has blown.

    Show answer
    Model answer: Remove the fuse and touch one probe on each metal end cap. A good fuse gives a reading close to 0 Ω (or the meter beeps). A blown fuse gives no continuity: the meter shows 'OL' or a very high resistance.
    Common mistakeLearners sometimes test the fuse while it is still in a live circuit; the test must be done with the supply off and the fuse removed.
  48. 48Short answer · ★ Challenge

    A technician has only three resistors: 4 Ω, 6 Ω and 12 Ω. Show how she can use all three together to obtain (a) the largest possible resistance and (b) the smallest possible resistance, and calculate each value.

    Show answer
    Model answer: (a) All three in series: R = 4 + 6 + 12 = 22 Ω. (b) All three in parallel: 1/R = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12, so R = 2 Ω.
    Common mistakeLearners often forget to turn 1/R upside down and give 0.5 Ω; 6/12 is 1/R, so R = 12/6 = 2 Ω.
  49. 49Short answer

    The earth electrode of a house is a copper rod driven deep into moist soil. Explain why it is placed in moist ground rather than laid on dry rock.

    Show answer
    Model answer: Moist soil conducts electricity much better than dry rock, so the earth connection has a low resistance. In a fault a large current can then flow to earth quickly, blowing the fuse or tripping the breaker before anyone is hurt.
    Common mistakeLearners sometimes say the rod must be wet to keep it cool; the reason is low resistance to the ground, not cooling.
  50. 50Short answer · ★ Challenge

    A 2.0 kW water heater has a thermostat, so it is actually heating for only 40 % of the 5 hours it is switched on each day. Calculate the energy it uses per day and the daily cost at 200 RWF per kWh (assume this price).

    Show answer
    Model answer: Heating time = 0.40 × 5 = 2.0 h. E = Pt = 2.0 kW × 2.0 h = 4.0 kWh. Cost = 4.0 × 200 = 800 RWF per day.
    Common mistakeLearners often use the full 5 h and get 10 kWh; the heater only uses energy while the thermostat has it switched on.