Chapter 5 — Electricity and magnetism
Charge, current and a complete path
Electric charge is a property of matter. Like charges repel, unlike charges attract, and charge is conserved in ordinary interactions. A current is the rate at which charge passes a chosen cross-section: I = Q/t for a steady rate, where Q is charge and t is time. One ampere is one coulomb per second. If 12 C of charge passes a wire cross-section in 4 s, average current is 3 A. The equation does not say that each electron travels from one end of a long wire to the other in one second; it records how much charge crosses a section per time.
A simple conducting loop must be closed for a steady current driven by a cell. An open switch breaks the conducting path. A circuit diagram uses symbols so that connections are unambiguous; a pretty drawing of a battery and bulb can hide whether the wire actually returns to the battery. Trace a path from one cell terminal through each component back to the other terminal. If that path is broken, the idealised circuit has no sustained current. Current direction is conventionally drawn from positive to negative outside the source, although electrons in a metal drift in the opposite direction. Do not reverse an ammeter reading merely because the mobile particles are electrons.
Potential difference, or voltage, is energy transferred per unit charge between two points: V = W/Q. One volt is one joule per coulomb. A source may maintain a potential difference across a circuit, making charge flow when a conducting path exists. Voltage is measured between points, so a voltmeter is connected in parallel with the component whose potential difference is sought. An ammeter measures current through a component and is connected in series with that path. Ideal meters simplify calculations: an ideal voltmeter draws negligible current, and an ideal ammeter adds negligible resistance. Real meters approximate rather than exactly achieve those ideals.
Resistance and the correct use of Ohm's law
Resistance relates voltage and current for an ohmic conductor held under the conditions where its resistance remains approximately constant: V = IR. One ohm is one volt per ampere. If a 6 Ω resistor has 12 V across it, current is 12/6=2 A. If voltage doubles and the resistor's temperature and physical state are assumed unchanged, current doubles. A filament lamp can heat substantially as voltage rises, changing its resistance; it need not give a perfectly straight V–I graph over a wide range. The exam phrase “ohmic resistor” or “constant resistance” signals when simple proportionality is expected.
Resistance of a uniform wire depends on its material, length and cross-sectional area: R = ρL/A, where ρ is resistivity. Longer wire means greater resistance if all else is fixed; larger cross-sectional area means lower resistance. Doubling both L and A leaves R unchanged in this ideal model. Resistivity is a material property at a stated temperature, not the resistance of any arbitrary piece of that material. Avoid answering a geometry question with “resistivity doubles” when only the wire's dimensions have changed.
In a series connection, components share the same current and their potential differences add. Ideal resistances add: R_total = R₁+R₂. Two resistors of 2 Ω and 4 Ω in series have 6 Ω equivalent resistance. Across a 12 V source, current is 12/6=2 A; voltage drops are 4 V and 8 V respectively. The bigger resistor has the bigger voltage drop in this series case. A student who assigns 12 V to each resistor has confused series with parallel.
In a parallel connection, branches share the same potential difference while branch currents add at the junction. For two ideal resistors, 1/R_total = 1/R₁+1/R₂. The same 2 Ω and 4 Ω connected in parallel across 12 V carry 6 A and 3 A, respectively, for a total 9 A. Equivalent resistance is 12/9 = 4/3 Ω, less than either branch resistance. A parallel addition creates another path for current; it should not increase equivalent resistance above both branch values. Use this qualitative check before trusting arithmetic.
Electrical power and energy
Power transferred in a circuit is P = VI. For an ohmic resistor under appropriate conditions, substitution gives P = I²R = V²/R. These forms agree only when the voltage, current and resistance describe the same component and state. A 12 V source supplying 2 A provides 24 W to the circuit in the idealised model. Over 10 s, the energy transferred is 24×10=240 J. Do not answer an energy question with 24 W; watts measure rate, joules measure amount. A kilowatt-hour is also an energy unit: 1 kWh = 3.6×10⁶ J.
Joule heating occurs when electrical energy is dissipated as thermal energy in a conductor with resistance. For constant current and resistance over time t, H = I²Rt. If current doubles while R and t stay fixed, heating becomes four times as large. An electric heater intentionally uses this effect. In power transmission, unwanted heating of wires is one reason that current levels matter. The school-level statement is about a model with specified conditions; changing the current can also change temperature and resistance in a real conductor, so do not infer exact real-world energy losses without those conditions.
Circuit safety as a concept
A fuse or circuit breaker interrupts a circuit when conditions exceed its design threshold, helping reduce overheating risk. A fuse wire melts under excessive current; a suitable breaker trips by its mechanism. An earth connection offers a protective low-resistance path under certain fault conditions, but it is not a substitute for insulation, a correctly rated protective device or proper installation. This book describes exam-level principles and does not instruct readers to repair live electrical equipment. A question may ask why household loads are normally arranged in parallel: each receives the supply potential difference and can operate independently within the circuit design. A series chain would cause one break to interrupt all loads and would divide the potential difference among them.
Magnetic field and moving charge
A magnet has north and south poles. Like poles repel; unlike poles attract. Magnetic field lines are a visual way to represent direction and relative strength of a field. Outside a bar magnet, their conventional direction runs from north to south; the field forms closed loops when the interior path is included. Closer line spacing in a drawing indicates a stronger field region. The lines are not physical threads. A compass needle aligns approximately with the local field direction, and nearby currents or ferromagnetic objects can alter that local field.
An electric current produces a magnetic field around a conductor. For a long straight wire, the field circles the wire; reversing current direction reverses field direction. A coil concentrates the field pattern and can act like a magnet while current flows. An electromagnet can be controlled by the circuit, unlike a permanent magnet whose field persists without a supply. A magnetic effect does not imply that every current-carrying wire will visibly pull a metal object: strength depends on current, geometry and material.
A current-carrying conductor in a magnetic field can experience a force. This is the basis of a simple electric motor, which converts electrical energy to mechanical motion. By contrast, changing magnetic flux through a circuit can induce an emf and, if the circuit is closed, a current. This is a generator principle, converting mechanical work into electrical energy in an idealised energy-flow description. A stationary magnet near a stationary coil does not produce a continuing induced current merely because a magnetic field exists; change in flux is central. A moving magnet, moving coil or changing current in a nearby coil can create that change.
Follow charge and energy separately
Current records charge flow, while voltage records energy transferred per unit charge. Suppose a circuit carries 0.5 A for 2 minutes. First convert time to 120 s; charge passed is Q=It=0.5×120=60 C. If the potential difference across a resistor is 6 V, the energy transferred there is W=VQ=6×60=360 J. The power route gives the same result: P=VI=6×0.5=3 W and W=Pt=3×120=360 J. These two routes provide a useful independent check. An option of 6 C probably used 12 s instead of 120 s; an option of 3 J probably confused power with energy. Write the requested quantity and unit before choosing a formula.
Charge is not consumed by a resistor. In a steady series circuit, the same amount of charge passes each cross-section per second. The source transfers energy to charges, and components transfer electrical energy into other forms. A bulb does not use up the current so that less charge returns to the cell. In a parallel circuit, the current divides among branches and recombines, so the sum entering an ordinary junction equals the sum leaving when charge is not accumulating there. If 5 A enters a junction and one branch carries 2 A away, a second outgoing branch must carry 3 A. This is charge conservation, not a claim that every branch receives equal current.
The direction of conventional current was defined using positive charge. In a metal, the mobile charge carriers are electrons and their drift is opposite to that convention. The physical circuit does not behave differently because a diagram uses conventional arrows. When comparing two diagrams, choose one convention consistently. In an electrolyte, both positive and negative ions may contribute to current, moving in opposite directions; the definition of current therefore cannot be reduced to “electrons always moving through every conductor.” For the simple metal-wire problems here, conventional current is the direction used in the circuit arrows.
Diagnose series and parallel connections
Two resistors are in series when the current through one must pass through the other without a branching path between them. Their placement next to each other on paper does not establish a series connection. Components are in parallel when their terminals connect to the same two circuit nodes. They may be drawn far apart and still share the same potential difference. Label the nodes before calculating. A wire drawn around a resistor can bypass it; an ideal conducting bypass across its terminals sets nearly zero voltage across that resistor in the simplified model. Counting resistor symbols without tracing connections can therefore produce an entirely wrong equivalent resistance.
Consider a 2 Ω resistor in series with a parallel combination of 6 Ω and 3 Ω across an ideal 12 V source. The parallel portion has equivalent resistance (6×3)/(6+3)=2 Ω. Total resistance is 2+2=4 Ω, so source current is 12/4=3 A. The series resistor drops 3×2=6 V, leaving 6 V across both parallel branches. Their currents are 6/6=1 A and 6/3=2 A, adding to the source current of 3 A. Check power as well: the series resistor dissipates 3²×2=18 W, the 6 Ω branch 6 W and the 3 Ω branch 12 W, giving 36 W altogether. Source power is 12×3=36 W. Agreement checks both the connections and arithmetic.
An ideal ammeter has negligible resistance so that inserting it in series changes the measured current as little as possible. An ideal voltmeter has extremely high resistance so that connecting it across a component draws negligible current. The meter symbol alone does not determine what is measured: its connection does. A voltmeter connected across a whole series pair reads the sum of their potential differences, while one connected across a single resistor reads only that drop. Practical meters and circuits have limits; these model statements explain the exam diagrams and are not instructions for experimenting with mains electricity.
Decide what stays fixed before comparing heating
The expressions P=I²R and P=V²/R appear to predict opposite effects when resistance increases. They describe different controlled comparisons. If current is held fixed, doubling resistance doubles power. If voltage is held fixed, doubling resistance halves power because current falls. A question that says “connected to the same ideal battery” usually fixes the voltage across the specified load, whereas “the same current passes through both resistors” fixes current. Read that condition before deciding which resistance becomes hotter. Temperature also depends on heat loss, mass and material, so power alone does not always determine the final temperature of unlike objects.
For two resistors of 2 Ω and 8 Ω in series, the same current flows through both, and their dissipated-power ratio is 2:8=1:4. In parallel across the same voltage, their powers are in the inverse ratio: 1/2:1/8=4:1. These two answers are both correct for their respective arrangements. A common wrong answer carries the series ratio into a parallel diagram. As a check, the lower-resistance parallel branch carries more current at the same voltage and therefore receives more power. In series, the higher-resistance component has the larger voltage drop at the shared current.
Read magnetic direction without guessing
For a straight current-carrying wire, the right-hand grip rule links current and magnetic-field direction. Point the right thumb in the conventional-current direction; the curled fingers indicate the circular field direction around the wire. Reversing the current reverses that direction. The magnetic field is not directed along the wire in this model. For a current loop or solenoid, the field pattern resembles that of a bar magnet near the coil, with its polarity determined by the current direction. The diagram must show how the current circulates before a pole can be named.
Electromagnetic induction depends on a changing magnetic flux through a circuit. Moving a magnet toward a coil can produce an induced emf; stopping it at a fixed position removes the continuing change in the simple stationary arrangement. Moving it away reverses the change and can reverse the induced current. A faster change can produce a larger induced emf under otherwise comparable conditions. Lenz's law specifies that the induced effect opposes the change producing it. It does not mean that an induced magnetic field always points opposite to the original field: the direction depends on whether the original flux is increasing or decreasing. This distinction is often clearer when tested with approaching and receding magnets as separate cases.
Retrieval exercise with worked checks
Hide this paragraph after reading the questions. A steady 2 A current flows for 30 s: how much charge passes? A 10 Ω resistor has 5 V across it: what are its current and power? Two 4 Ω resistors are connected in parallel: what is their equivalent resistance? The checks are 60 C, 0.5 A, 2.5 W and 2 Ω respectively. For the power, either VI=5×0.5 or V²/R=25/10 works. For the parallel pair, equal branches halve the resistance. Explain each operation in words before looking at the numbers; a correct guess without the circuit relationship is not yet secure recall.
Worked circuit and field example
Consider a synthetic 6 V cell connected to two resistors, 3 Ω and 6 Ω, in parallel. Each branch has 6 V across it. Currents are 6/3=2 A and 6/6=1 A, so source current is 3 A. Source power is VI = 6×3=18 W. The equivalent resistance is V/I = 6/3=2 Ω, lower than the 3 Ω smaller branch. If the same resistors were placed in series, total resistance would be 9 Ω and current would be 6/9≈0.67 A. The two arrangements use the same components but answer very different questions. Sketch the connections before calculating.
Now imagine placing a compass near one straight segment of that circuit. A steady current produces a magnetic field that can deflect the needle. Opening the switch stops the sustained current and removes that current-produced field in the idealised account. Reversing the cell polarity reverses the current and the direction of the current-produced field. The circuit diagram and the magnetic-field idea therefore connect: first establish whether a current flows and in which direction, then infer its magnetic effect.
Recall before choosing options
Write the units for charge, current, potential difference, resistance, power and energy. Explain why an ammeter belongs in series and a voltmeter in parallel. State what stays equal in series and in parallel. For a fixed resistor, calculate the current at 12 V if it is 6 Ω, then check the unit. Describe one energy conversion in a motor and one in a generator. Finally, state what must change to induce an emf. These prompts expose understanding more reliably than memorising a row of instrument names.
Figure 5. Original chapter diagram.
Practice 36 questions
Choose one answer for each item. The answer key and explanations follow this chapter set.
1. Which scientist established the relationship V = IR between the voltage, current and resistance of a conductor?
A. André-Marie Ampère B. Alessandro Volta C. James Prescott Joule D. Georg Simon Ohm
2. What is the SI unit of electric charge?
A. Ampere B. Volt C. Coulomb D. Farad
3. Which of the following is NOT a semiconductor?
A. Silicon B. Copper C. Germanium D. Gallium arsenide
4. Which device is used to step up or step down an alternating voltage?
A. Rectifier B. Galvanometer C. Transformer D. Electric motor
5. Who discovered electromagnetic induction in 1831?
A. Hans Christian Oersted B. André-Marie Ampère C. Michael Faraday D. Nikola Tesla
6. Assertion (A): Electrical appliances in a house are connected in parallel.
Reason (R): In a parallel connection each appliance receives the same voltage and can be switched off without affecting the others.
Select the correct option.
A. Both A and R are true and R is the correct explanation of A B. Both A and R are true but R is not the correct explanation of A C. A is true but R is false D. A is false but R is true
7. A mobile phone charger must convert AC from the wall socket into DC for the battery. The circuit that does this conversion is called a:
A. Inverter B. Rectifier C. Transformer D. Galvanometer
8. Electroplating a thin metal layer onto an object is an application of which effect of electric current?
A. Heating effect B. Magnetic effect C. Photoelectric effect D. Chemical effect
9. Which protective device trips on overload or short circuit and can be reset after the electrical fault has been corrected, rather than replaced like a blown fuse?
A. Fuse B. Rectifier C. Step-down transformer D. Miniature Circuit Breaker (MCB)
10. Ohm's law (V = IR) holds for a metallic conductor provided which of the following remains constant?
A. Current B. Temperature C. Voltage D. Power
11. Match each traditional component with a commonly associated material in the school-level examples. List I: A. Incandescent filament; B. Heater element; C. Traditional low-melting fuse wire; D. Household conducting wire. List II: 1. Copper; 2. Tin–lead alloy; 3. Tungsten; 4. Nichrome.
A. A-4, B-3, C-2, D-1 B. A-3, B-2, C-4, D-1 C. A-3, B-4, C-2, D-1 D. A-1, B-4, C-2, D-3
12. In a 50 Hz AC supply, how many times does the current reverse its direction in one second?
A. 100 B. 50 C. 25 D. 200
13. What is the frequency of the alternating current (AC) supplied to Indian households?
A. 60 Hz B. 100 Hz C. 220 Hz D. 50 Hz
14. A 1500 W geyser is used for 2 hours every day. How many units (kWh) of electricity does it consume in 30 days?
A. 90 units B. 45 units C. 3 units D. 900 units
15. At the same temperature, a wire has resistance R. Another wire of the same material has twice its length and twice its diameter. What is its resistance?
A. 2R B. R/2 C. R/4 D. 4R
16. Resistors of 10 Ω and 20 Ω are connected in series across a 6 V battery. What is the potential difference across the 20 Ω resistor?
A. 2 V B. 6 V C. 3 V D. 4 V
17. A steady current of 3 A flows through a wire for 10 s. How much charge passes through any cross-section of the wire in this time?
A. 13 C B. 0.3 C C. 30 C D. 3 C
18. Two resistors of 6 Ω each are connected in parallel. What is their equivalent resistance?
A. 12 Ω B. 3 Ω C. 6 Ω D. 1.5 Ω
19. In a standard three-pin plug, the thickest pin is connected to the:
A. Earth wire B. Live wire C. Neutral wire D. Fuse wire
20. Nichrome, used in the heating elements of irons and heaters, is an alloy of:
A. Nickel and copper B. Iron and chromium C. Nickel and chromium D. Tin and lead
21. A 12 Ω resistor is connected directly across an ideal 6 V source. What power does it dissipate?
A. 0.5 W B. 18 W C. 72 W D. 3 W
22. Which metal is commonly used for overhead long-distance power transmission lines because it is lighter and cheaper than copper?
A. Silver B. Aluminium C. Tungsten D. Nichrome
23. The deliberate addition of small amounts of impurity to a semiconductor such as silicon, to control its conductivity, is called:
A. Doping B. Annealing C. Galvanisation D. Vulcanisation
24. For ordinary direct-reading meters in a simple school circuit, consider these statements. Statement I: An ammeter is connected in parallel with the component whose current it measures. Statement II: A voltmeter is connected in parallel across the component whose potential difference it measures. Which statement(s) is/are correct?
A. Only I B. Only II C. Both I and II D. Neither I nor II
25. Consider the following statements:
Statement I: In a series circuit, the same current flows through every resistor.
Statement II: The equivalent resistance of resistors in parallel is greater than the largest individual resistance.
Which of the above statements is/are correct?
A. Only I B. Only II C. Both I and II D. Neither I nor II
26. For ideal positive-valued resistors, Statement I: In a parallel circuit the same current flows through every branch. Statement II: The equivalent resistance of resistors in parallel is less than the smallest individual resistance. Which statement(s) is/are correct?
A. Only I B. Only II C. Both I and II D. Neither I nor II
27. Which of the following devices does NOT work on the heating effect of electric current?
A. Electric toaster B. Filament bulb C. Electric iron D. Electric motor
28. Which of the following is NOT an electrical insulator?
A. Mica B. Glass C. Aluminium D. Dry wood
29. Which of the following statements about a fuse is NOT correct?
A. It is connected in series with the live wire B. It works by regulating the current to a constant safe value C. Its wire is made of a low-melting-point alloy such as tin-lead D. It melts and breaks the circuit when the current exceeds a safe limit
30. Resistors of 3 Ω and 6 Ω are connected in parallel across an ideal 6 V source. What is the total current supplied?
A. 3 A B. 1 A C. 2 A D. 9 A
31. Arrange the following discoveries in the correct chronological order.
A. Faraday's discovery of electromagnetic induction
B. Oersted's observation that a current deflects a compass needle
C. Lenz's statement of the law for the direction of an induced current
D. Volta's invention of the voltaic pile
A. D, B, A, C B. B, D, A, C C. D, A, B, C D. D, B, C, A
32. In a simple DC electric motor, which component reverses the direction of current in the coil every half rotation so that the coil keeps rotating in one direction?
A. Slip rings B. Split-ring commutator C. Soft iron armature core D. Permanent field magnet
33. Which of the following uses powerful electromagnets to float above the track and propel itself, almost eliminating wheel friction?
A. Diesel-locomotive train B. Maglev train C. Electric locomotive with a pantograph D. Rack railway
34. The law stating that the direction of an induced current is always such that it opposes the change that produced it is known as:
A. Faraday's first law B. Ampere's circuital law C. Coulomb's law D. Lenz's law
35. Which rule gives the direction of the force on a current-carrying conductor placed in a magnetic field, as used for electric motors?
A. Fleming's left-hand rule B. Fleming's right-hand rule C. Maxwell's right-hand thumb rule D. Lenz's law
36. The magnetic field inside a long current-carrying solenoid is:
A. Zero everywhere inside B. Concentric circles around the axis C. Strongest at the centre and zero near the ends D. Strong and nearly uniform along its axis
Answers and explanations
1. D. Georg Simon Ohm established that, at constant temperature, the current through a conductor is proportional to the voltage across it, V = IR; the unit of resistance, the ohm, is named after him. Ampère, Volta and Joule are honoured by the units of current, potential difference and energy.
2. C. The SI unit of electric charge is the coulomb (C); one coulomb is the charge carried past a point by a current of one ampere in one second (1 C = 1 A·s). Ampere is the unit of current, volt of potential difference and farad of capacitance.
3. B. Silicon and germanium are the two most important semiconductors, forming the backbone of transistors, diodes and chips; gallium arsenide is another. Copper is a conductor with plenty of free electrons, so it is the odd one out.
4. C. A transformer raises (step-up) or lowers (step-down) an alternating voltage using electromagnetic induction; it works only with AC because it needs a changing magnetic field. A rectifier converts AC to DC, a motor converts electrical to mechanical energy and a galvanometer detects small currents.
5. C. Michael Faraday discovered in 1831 that a changing magnetic field induces a current in a conductor, the principle behind generators and transformers. Oersted (1820) had shown the opposite effect, that a current produces a magnetic field.
6. A. Household wiring is parallel, so every appliance gets the same voltage and one can be switched off or fail without cutting power to the rest. In a series loop a single dead bulb would break the only path. Both A and R are true and R explains A.
7. B. A rectifier converts AC into DC. An inverter does the reverse (DC to AC), a transformer only steps AC voltage up or down, and a galvanometer detects small currents.
8. D. Electroplating uses a current to drive an electrochemical change that deposits metal on a suitable object. This is the chemical effect of electric current. A battery is different: its chemical reactions produce a potential difference that can drive current, so it should not be described as a device powered by the chemical effect of an external current.
9. D. A miniature circuit breaker (MCB) interrupts the circuit during a suitable overload or short-circuit fault. After the cause is corrected, it can be reset. A melted fuse element normally needs replacement; neither a rectifier nor a transformer serves this protection function.
10. B. Ohm's law says current is proportional to voltage at constant temperature, since the resistance of most metals rises when they heat up. Current and voltage are the variables that change together, so they cannot be the fixed condition.
11. C. A tungsten filament withstands high temperature; a nichrome heater has suitable resistivity and resists oxidation; a traditional fuse can use a low-melting tin–lead alloy; and copper is a common conductor for household wiring. Thus A-3, B-4, C-2, D-1. Actual components vary by design and current standards.
12. A. Each cycle has two reversals of direction. With 50 cycles per second, the current reverses 50 × 2 = 100 times every second. Picking 50 confuses cycles with reversals.
13. D. The nominal frequency of ordinary Indian AC supply is 50 Hz. Frequency counts complete cycles per second; voltage is a different quantity. The value was checked against Indian electricity-standard and CEA material.
14. A. Power = 1500 W = 1.5 kW. Daily energy = 1.5 kW × 2 h = 3 kWh. For 30 days: 3 × 30 = 90 kWh = 90 units. One unit on the bill is 1 kWh.
15. B. Resistance R = ρl/A rises with length and falls with cross-sectional area. Doubling the length doubles R, while doubling the diameter makes the area 2² = 4 times, dividing R by 4. Net effect: R × 2 ÷ 4 = R/2.
16. D. In series the resistances add: 10 + 20 = 30 Ω, so I = V/R = 6/30 = 0.2 A, the same in both resistors. The potential difference across the 20 Ω resistor is IR = 0.2 × 20 = 4 V (and 2 V across the 10 Ω resistor; the two add up to 6 V).
17. C. Current is the rate of flow of charge: 1 A means 1 C per second. So the charge = current × time = 3 A × 10 s = 30 C. The coulomb is the SI unit of charge.
18. B. For parallel resistors 1/R = 1/6 + 1/6 = 2/6, so R = 3 Ω. This is less than either resistor, as parallel combinations always are. 12 Ω would be the series value.
19. A. In a common three-pin plug, the thicker and longer pin is the protective earth connection. It links an exposed conductive appliance case to the earthing system so a suitable fault can be cleared by protective equipment. It is not the normal live or neutral supply pin.
20. C. Nichrome is a nickel-chromium alloy with high resistivity, a high melting point and resistance to oxidation, ideal for heating coils. Tin-lead is fuse wire; nickel-copper alloys are constantan-type.
21. D. For a resistor across 6 V, P = V²/R = 6²/12 = 36/12 = 3 W. Equivalently, I = V/R = 0.5 A and P = VI = 3 W. The resistance and source voltage are specified, so the result does not require any assumption about another branch.
22. B. Aluminium conducts well, is much lighter than copper and cheaper, so it is used (usually steel-reinforced) in overhead lines. Silver is too costly, tungsten is for filaments and nichrome is a high-resistance heating alloy.
23. A. Doping adds impurity atoms to a pure semiconductor to raise and control its conductivity, making diodes and transistors possible. Annealing is heat treatment, galvanisation is zinc coating, vulcanisation hardens rubber.
24. B. For the stated conventional circuit, an ammeter is placed in series so the measured branch current passes through it; Statement I is false. A voltmeter is placed in parallel across the two points of interest; Statement II is true. Other current-sensing technologies exist, so the instrument context is specified.
25. A. Statement I is correct: a series circuit has a single path, so the current is the same everywhere. Statement II is wrong: parallel resistance is always less than the smallest individual resistance, because extra paths are added.
26. B. In a parallel circuit every branch gets the same voltage while the current divides among the branches according to their resistance, so Statement I is false. Extra paths for the current lower the total resistance below that of the smallest resistor, so Statement II is true.
27. D. An electric motor works on the magnetic effect of current, converting electrical energy into mechanical energy. Toasters, irons and filament bulbs all use the heating effect in a resistive wire or filament.
28. C. Aluminium is a good conductor, which is why it is used in overhead power transmission lines. Mica, glass and dry wood have tightly bound electrons and block current, so they act as insulators.
29. B. A fuse is a low-melting-point wire (commonly tin-lead) placed in series with the live wire; on a short circuit or overload it melts and breaks the circuit, and must then be replaced. It does not regulate or limit the current to a set value.
30. A. In parallel, each resistor has 6 V across it. The branch currents are 6/3 = 2 A and 6/6 = 1 A, so total current is 3 A. Equivalently, equivalent resistance is 2 Ω and I = 6/2 = 3 A.
31. A. Volta's voltaic pile came in 1800, Oersted showed in 1820 that a current deflects a compass needle, Faraday discovered electromagnetic induction in 1831 and Lenz stated his law in 1834. So the order is D, B, A, C.
32. B. The split-ring commutator reverses the current each half turn, keeping the torque in one direction. Slip rings are used in AC generators and do not reverse current; the armature core and field magnet do not switch current at all.
33. B. A maglev (magnetic levitation) train is lifted above its track and driven forward by powerful electromagnets, so wheel friction is almost eliminated and very high speeds are possible. The other options run on wheels in contact with the rails.
34. D. Lenz's law (1834) gives the direction of induced current: it always opposes its cause, a consequence of conservation of energy. Faraday's law gives the magnitude of induced EMF; Coulomb's law concerns force between charges.
35. A. Fleming's left-hand rule gives the force (motion) direction in motors. The right-hand rule gives induced-current direction in generators, and Maxwell's thumb rule gives the direction of the field around a straight current-carrying wire.
36. D. Inside a long solenoid the field lines are parallel and closely packed along the axis, so the field is strong and nearly uniform, like that inside a bar magnet. Concentric circles describe the field around a single straight wire.