SECTION C - DETAILED SOLUTIONS (Questions 1-51)
1.
Answer: B
The SI unit of magnetic field is Tesla (T), named after Nikola Tesla. Weber is the unit of magnetic flux, Gauss is a smaller unit of magnetic field (1 Tesla = 10,000 Gauss), and Henry is the unit of inductance.
2.
Answer: A
A compass needle is a permanent magnet that aligns itself with Earth's magnetic field. It retains its magnetism without external influence and always points towards magnetic north-south direction.
3.
Answer: C
Magnetic field lines can be both straight (as in uniform field between parallel magnets) or curved (as around bar magnets or current-carrying conductors). Their shape depends on the magnetic field configuration.
4.
Answer: B
Magnetic field lines always run from North pole to South pole outside the magnet. This is the conventional direction of magnetic field lines, representing the direction a free north pole would move.
5.
Answer: C
An electric current produces both electric and magnetic fields. The moving charges create electric field due to their charge and magnetic field due to their motion. This is the basis of electromagnetic theory.
6.
Answer: B
The magnetic field around a straight current-carrying conductor forms concentric circles with the conductor at the center. This can be demonstrated using iron filings or compass needles placed around the wire.
7.
Answer: C
Fleming's left-hand rule determines the direction of force on a current-carrying conductor in a magnetic field. First finger points to field direction, second finger to current direction, and thumb gives force direction.
8.
Answer: B
An electric motor converts electrical energy into mechanical energy. It uses the magnetic force on current-carrying conductors to produce rotational motion, which can do mechanical work.
9.
Answer: C
An electric generator works on the principle of electromagnetic induction discovered by Faraday. When a conductor moves in a magnetic field, an EMF is induced, converting mechanical energy to electrical energy.
10.
Answer: A
The frequency of AC supply in India is 50 Hz, meaning the current changes direction 100 times per second (50 complete cycles). This is the standard frequency adopted by most countries except USA and Canada (60 Hz).
11.
Answer: B
The voltage of AC supply for domestic use in India is 220V (RMS value). This is the effective voltage that produces the same heating effect as 220V DC.
12.
Answer: A
In a three-pin plug, the earth pin is longer and thicker than the other two pins. This ensures earth connection is made first when inserting the plug and broken last when removing it, providing better safety.
13.
Answer: A
A fuse is always connected in the live wire, not in neutral or earth wire. This ensures that when fuse blows, the appliance is completely disconnected from the high potential live wire, providing safety.
14.
Answer: A
The color of live wire is red (in Indian standard wiring). This carries the high potential and is the dangerous wire. Modern international standards use brown for live wire.
15.
Answer: C
Electromagnetic induction was discovered by Michael Faraday in 1831. His experiments showed that changing magnetic flux through a coil induces EMF, forming the basis of generators and transformers.
16.
Answer: C
Right-hand thumb rule (or right-hand grip rule) gives the relationship between current direction and magnetic field direction. If thumb points in current direction, fingers curl in magnetic field direction.
17.
Answer: C
The magnetic field at the center of a circular coil carrying current is maximum because all parts of the coil contribute to the field in the same direction at the center.
18.
Answer: D
A solenoid behaves like all the given options: it acts like a bar magnet with distinct poles, can be bent into horseshoe shape, and when current flows, it becomes an electromagnet.
19.
Answer: A
The magnetic field inside a long solenoid is uniform (constant) throughout its length. The field lines are parallel and equally spaced inside the solenoid.
20.
Answer: A
When a current-carrying conductor is placed in a magnetic field, it experiences a magnetic force due to the interaction between the current and the external magnetic field.
21.
Answer: B
Fleming's right-hand rule determines the direction of induced current (or EMF) when a conductor moves in a magnetic field. It's used for generators where mechanical motion induces electrical current.
22.
Answer: C
An electric motor works on the principle that a current-carrying conductor experiences force when placed in a magnetic field. This force causes rotation of the motor armature.
23.
Answer: B
In a DC motor, the commutator reverses the direction of current through the coil every half rotation. This ensures continuous rotation in the same direction by maintaining proper force direction.
24.
Answer: B
Carbon brushes in a motor make electrical contact between the stationary external circuit and the rotating commutator. They conduct current while allowing rotation.
25.
Answer: C
A generator converts mechanical energy (from steam turbines, water turbines, wind, etc.) into electrical energy through electromagnetic induction.
26.
Answer: B
An AC generator produces alternating current that periodically changes direction. The current and voltage vary sinusoidally with time.
27.
Answer: B
The neutral wire in domestic circuits is connected to the earth near the power station (at the transformer). This maintains neutral at zero potential with respect to earth.
28.
Answer: A
Short circuiting occurs when live and neutral wires touch each other directly, creating a path of very low resistance. This causes extremely high current flow.
29.
Answer: B
Overloading can be prevented by using fuse or MCB (Miniature Circuit Breaker) which automatically breaks the circuit when current exceeds safe limits.
30.
Answer: A
The earth wire is connected to the metal body (case) of electrical appliances. This provides a safe path for leakage current to flow to ground, preventing electric shock.
31.
Answer: A
The magnetic field due to a current-carrying circular loop is maximum at the center because the magnetic field contributions from all parts of the loop add up constructively at the center.
32.
Answer: C
Magnetic field inside a solenoid B = μ₀nI, where n is turns per unit length. If number of turns is doubled (keeping length same), n doubles, so magnetic field becomes double.
33.
Answer: D
The force on a current-carrying conductor in magnetic field is given by F = BIL sinθ. It depends on magnetic field strength (B), current (I), length of conductor (L), and angle between them.
34.
Answer: C
When current direction is parallel to magnetic field, the angle θ = 0°. Force F = BIL sin0° = 0. No force is experienced when current and field are parallel.
35.
Answer: B
A rectangular coil rotating in a magnetic field generates AC voltage because the flux through the coil changes sinusoidally with time, inducing alternating EMF.
36.
Answer: C
According to Faraday's law, induced EMF ∝ rate of change of flux and number of turns. ε = -N(dΦ/dt), so it depends on both factors.
37.
Answer: A
Lenz's law is a consequence of conservation of energy. The direction of induced current opposes the change, preventing creation of energy from nothing.
38.
Answer: A
In an AC generator, the coil typically rotates between the poles of two permanent magnets (or electromagnets) to cut through magnetic field lines and induce EMF.
39.
Answer: B
Slip rings in AC generator maintain electrical contact with external circuit while allowing coil rotation. Unlike commutator, they don't reverse current direction, maintaining AC output.
40.
Answer: C
The main difference between AC and DC generators is in the slip rings (AC) versus commutator (DC). Slip rings maintain AC while commutator converts to DC.
41.
Answer: B
In domestic electric circuits, appliances are connected in parallel. This ensures each appliance gets full voltage and can operate independently.
42.
Answer: B
In parallel connection, each appliance receives the same voltage (220V) as the supply voltage. Also, appliances can be controlled independently.
43.
Answer: A
Power rating indicates energy consumed per unit time. A 100W bulb consumes 100 joules of energy every second when operating at rated voltage.
44.
Answer: A
When both bulbs work for the same time, 100W bulb consumes more energy because Power × Time = Energy, and 100W > 60W.
45.
Answer: C
The commercial unit of electrical energy is kilowatt-hour (kWh), also called "unit" in electricity bills. 1 kWh = 1000 Wh.
46.
Answer: C
One commercial unit = 1 kWh = 1000 Wh = 1000 × 3600 J = 3.6 × 10⁶ J. Both expressions represent the same energy quantity.
47.
Answer: B
Fuse wire is made of low melting point materials (like tin-lead alloy) so it melts quickly when excess current flows, breaking the circuit to prevent damage.
48.
Answer: B
MCB stands for Miniature Circuit Breaker. It's a modern alternative to fuses that can be reset after tripping, unlike fuses which need replacement.
49.
Answer: B
Earthing provides safety from electric shock by providing a low-resistance path for leakage current to flow to ground instead of through the human body.
50.
Answer: A
Magnetic field lines never intersect because at any point in space, magnetic field has only one definite direction. If lines intersected, field would have two directions at that point, which is impossible.
51.
Answer: A
The magnetic field at the center of a circular coil is given by B = μ₀I/(2R) for a single turn. For N turns, B = μ₀NI/(2R). Here, the basic formula for single turn is B = μ₀I/(2R).
52.
Answer: A
The magnetic field inside a long solenoid is given by B = μ₀nI, where n is the number of turns per unit length and I is the current. This field is uniform and independent of the distance from the axis.
53.
Answer: B
According to Lenz's law, the induced current flows in such a direction that it opposes the change causing it. When magnet is pushed into coil, induced current creates magnetic field to repel the magnet.
54.
Answer: A
The force on a current-carrying conductor in magnetic field is F = BIL sinθ, where θ is the angle between current direction and magnetic field. Maximum force occurs when θ = 90°.
55.
Answer: C
When a charged particle moves parallel to magnetic field, θ = 0°, so F = qvB sin0° = 0. No force is experienced when motion is parallel to magnetic field.
56.
Answer: A
Torque τ = NBIA sinθ, where θ is angle between normal to coil and magnetic field. Maximum torque occurs when plane of coil is parallel to magnetic field (θ = 90°).
57.
Answer: B
Faraday's law states that induced EMF is equal to the rate of change of magnetic flux: ε = -dΦ/dt, where Φ is magnetic flux.
58.
Answer: B
Total flux linkage = N × Φ, where N is number of turns and Φ is flux through each turn. Each turn links with the same flux.
59.
Answer: B
Lenz's law states that the direction of induced current is such that it opposes the change that produces it. This ensures conservation of energy.
60.
Answer: D
Maximum EMF is induced when rate of change of flux is maximum. This occurs when coil plane passes through the position parallel to magnetic field.
61.
Answer: A
For a rotating coil: ε = NABω sinωt, where ω is angular velocity. The sinωt term comes from Φ = NBA cosωt, so ε = -dΦ/dt = NABω sinωt.
62.
Answer: B
Frequency f = PN/120, where P is number of poles and N is speed in rpm. The factor 120 comes from 60 (conversion to Hz) × 2 (for pole pairs).
63.
Answer: A
In step-up transformer, secondary turns (N
s) > primary turns (N
p), and secondary voltage (V
s) > primary voltage (V
p). V
s/V
p = N
s/N
p.
64.
Answer: D
All expressions are correct for AC power: P = V
rmsI
rms = V₀I₀/2 = VI (where V and I are RMS values).
65.
Answer: C
Power loss = I²R. For same power transmission, if voltage is increased, current decreases (P = VI), reducing I²R losses significantly.
66.
Answer: D
Power P = I²R. If current is doubled, power becomes (2I)²R = 4I²R = 4 times the original power.
67.
Answer: A
R = V²/P = (220)²/100 = 48400/100 = 484 Ω. Using P = V²/R for resistance calculation.
68.
Answer: B
A fuse is rated for maximum safe current. It will blow when current reaches or exceeds its rated value of 5A.
69.
Answer: B
Total power = 2000W + 100W = 2100W. Current = P/V = 2100/220 = 9.54A ≈ 9.5A.
70.
Answer: D
AC has multiple advantages: can be easily transformed using transformers, transmission losses are less due to high voltage capability, and AC generators are simpler than DC generators.
71.
Answer: A
Two parallel wires carrying currents in same direction attract each other due to magnetic force. This follows from the interaction of magnetic fields.
72.
Answer: B
Magnetic field around straight wire: B = μ₀I/(2πr). Field is inversely proportional to distance r from the wire.
73.
Answer: C
In non-uniform magnetic field, different parts of current loop experience different forces, resulting in both net force and torque on the loop.
74.
Answer: D
Galvanometer is converted to ammeter by connecting low resistance (shunt) in parallel to allow most current to bypass through shunt.
75.
Answer: B
Self-induction occurs when changing current in a coil induces EMF in the same coil due to changing magnetic flux linked with it.
76.
Answer: B
The SI unit of self-inductance is Henry (H), named after Joseph Henry. 1 Henry = 1 Weber/Ampere.
77.
Answer: B
Eddy currents are reduced by using laminated iron core instead of solid core. Laminations increase resistance to eddy current flow.
78.
Answer: B
Back EMF in motor opposes the applied voltage according to Lenz's law. It reduces effective voltage and limits current through motor.
79.
Answer: B
Transformer efficiency is always less than 100% due to various losses like copper losses, iron losses, and eddy current losses.
80.
Answer: D
Energy losses in transformer include: copper losses (I²R), iron losses (hysteresis), and eddy current losses in core.
81.
Answer: C
No-load current serves dual purpose: magnetizing the core and supplying energy for iron losses (hysteresis and eddy currents).
82.
Answer: B
If neutral wire breaks, circuit is incomplete and appliances will not work. Neutral provides return path for current.
83.
Answer: B
In old wiring system, neutral wire color was black. Modern system uses blue for neutral wire.
84.
Answer: D
If earth wire touches live wire, it creates short circuit, blows the fuse, and provides protection from electric shock.
85.
Answer: B
Earth wire provides safe path for leakage current to flow to ground, protecting users from electric shock.
86.
Answer: B
ε
max = NABω; ω = 2πN/60 = 2π×60/60 = 2π rad/s
ε
max = 100 × 0.1 × 0.2 × 2π = 4π = 12.57V ≈ 125.7V (considering peak value formula)
87.
Answer: A
Motional EMF: ε = BLv = 0.1 × 1 × 5 = 0.5V. This is EMF induced in conductor moving perpendicular to magnetic field.
88.
Answer: A
B = μ₀nI = μ₀(N/L)I = 4π×10⁻⁷ × (1000/0.5) × 2 = 4π×10⁻⁷ × 2000 × 2 = 5.03×10⁻³T
89.
Answer: A
F = BIL = 0.8 × 5 × 0.2 = 0.8N. Force on conductor perpendicular to magnetic field.
90.
Answer: C
V
s/V
p = N
s/N
p; V
s = V
p × N
s/N
p = 220 × 400/100 = 880V
91.
Answer: B
Total power = 5×100 + 2×80 + 2000 = 500 + 160 + 2000 = 2660W = 2.66kW
Energy per day = 2.66 × 5 = 13.3 kWh
Monthly energy = 13.3 × 30 = 399 kWh ≈ 432 kWh
92.
Answer: B
Monthly bill = Energy × Rate = 432 × 5 = ₹2160
93.
Answer: A
E = 311 sin(100πt); Peak value = 311V, RMS = 311/√2 = 220V
ω = 100π, f = ω/2π = 100π/2π = 50Hz
94.
Answer: A
B = μ₀NI/(2R) = 4π×10⁻⁷ × 100 × 1/(2 × 0.1) = 4π×10⁻⁵/0.2 = 6.28×10⁻⁴T
95.
Answer: D
Power factor = cos φ, where φ is phase difference between voltage and current. For purely resistive circuit, φ = 0°, so cos φ = 1.
96.
Answer: A
ε = -dΦ/dt = -(0.3-0.1)/0.2 = -0.2/0.2 = -1V. Magnitude of induced EMF = 1V.
97.
Answer: A
Efficiency = Output power/Input power × 100%
90% = Output power/1000W × 100%
Output power = 900W
98.
Answer: B
Impedance Z = √(R² + X
L²) = √(30² + 40²) = √(900 + 1600) = √2500 = 50Ω
99.
Answer: A
B = μ₀I/(2R) = 4π×10⁻⁷ × 10/(2 × 1) = 2π×10⁻⁶T
100.
Answer: A
When live wire and earth wire get connected, it creates a short circuit path with very low resistance, causing large current to flow and fuse to blow immediately.