In a circuit with capacitors, which quantity is continuous across the capacitor?
Answer: C
In DC circuits, current is continuous (same) through all series elements including capacitors in steady state. However, in AC circuits, current flows through capacitors.
Q.182Medium
Which of the following shows non-ohmic behavior?
Answer: C
Tungsten filament's resistance increases significantly with temperature due to heating, causing non-linear I-V characteristic (non-ohmic).
Q.183Medium
In Joule heating, if voltage is doubled and resistance is halved, the power dissipated becomes:
Answer: C
P = V²/R. New P = (2V)²/(R/2) = 4V²×2/R = 8(V²/R) = 8P₀
Q.184Medium
A wire of length L and cross-sectional area A has resistance R. If the wire is stretched to 1.5 times its original length without change in volume, what will be its new resistance?
Answer: A
When stretched, length becomes 1.5L. Volume remains constant (LA = A'L'), so A' = A/1.5. New resistance R' = ρ(1.5L)/(A/1.5) = 2.25ρL/A = 2.25R
Q.185Medium
A heating element rated 1000W, 220V is connected to a 110V supply. The heat produced becomes:
Answer: A
Resistance of element R = V²/P = 220²/1000 = 48.4Ω (constant). At 110V: P' = V'²/R = 110²/48.4 ≈ 250W. Power varies with square of voltage.
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Q.186Medium
An electron enters a region of uniform magnetic field with velocity v perpendicular to the field. If the magnetic field strength is B, the radius of curvature is:
Answer: A
For a charged particle in a magnetic field, centripetal force equals magnetic force: mv²/r = evB, giving r = mv/eB. This is the radius of the circular path.
Q.187Medium
Two parallel wires carrying currents I₁ and I₂ in opposite directions are separated by distance d. The force between them is:
Answer: C
Currents in opposite directions repel each other. The force per unit length is F/ℓ = μ₀I₁I₂/2πd, making total force F = μ₀I₁I₂ℓ/2πd (repulsive).
Q.188Medium
A rectangular loop of dimensions a × b carrying current I is placed in a uniform magnetic field B. The maximum torque on the loop is:
Answer: A
Torque on a current loop in a magnetic field is τ = NIAB sin(θ), where A is the area and θ is the angle. Maximum torque occurs when sin(θ) = 1, giving τ_max = BIab for N=1.
Q.189Medium
The magnetic moment of an electron orbiting in the first Bohr orbit is approximately:
Answer: A
The magnetic moment of an electron in the first Bohr orbit equals 1 Bohr magneton (μ_B = eℏ/2m_e ≈ 9.27 × 10⁻²⁴ J/T). This is a fundamental quantum result.
Q.190Medium
The magnetic field due to a long straight wire carrying current I at perpendicular distance r is:
Answer: A
Using Ampere's law for a long straight wire, ∮B·dl = μ₀I_enclosed. For a circular path of radius r: B(2πr) = μ₀I, giving B = μ₀I/2πr.
Q.191Medium
A proton and an electron, both accelerated through the same potential difference, enter a uniform magnetic field perpendicularly. Which has a larger radius of curvature?
Answer: A
Both particles gain same kinetic energy, so mv²/2 is same. Since r = mv/eB and proton has much larger mass than electron, proton has larger radius of curvature.
Q.192Medium
The period of revolution of a charged particle in a magnetic field is independent of:
Answer: C
Period T = 2πm/eB is independent of velocity. This remarkable result means all particles with same m and q have same period regardless of speed in a given B field.
Q.193Medium
A compass needle placed in a magnetic field experiences a maximum torque when the needle is:
Answer: C
Torque τ = m × B has magnitude τ = mB sin(θ). Maximum occurs when sin(θ) = 1, i.e., θ = 90° (perpendicular orientation).
Q.194Medium
The self-inductance of a solenoid with N turns, length L, and cross-sectional area A is:
Answer: A
Self-inductance of solenoid is derived from L = NΦ/I where Φ = μ₀nIA. This gives L = μ₀N²A/L, proportional to N² and inversely proportional to length.
Q.195Medium
A solenoid with 500 turns is 0.5 m long and carries a current of 2 A. The permeability of free space is μ₀ = 4π × 10⁻⁷ T·m/A. Calculate the magnetic field inside the solenoid.
Answer: C
B = μ₀nI where n = N/L = 0500.5 = 1000 turns/m. B = 4π × 10⁻⁷ × 1000 × 2 = 2.51 × 10⁻¹ T ≈ 0.251 T.
Q.196Medium
Two parallel wires carry currents I₁ = 5 A and I₂ = 3 A in the same direction, separated by distance r = 0.1 m. The force per unit length between them is approximately:
A rectangular loop ABCD with sides 2 m × 3 m carries a current of 4 A and is placed in a uniform magnetic field of 0.5 T perpendicular to the plane of the loop. The magnetic torque on the loop is:
Answer: A
Torque τ = NIAB sin θ. When B is perpendicular to the plane of the loop, it is parallel to the normal of the loop area, so θ = 0° and τ = 0.
Q.198Medium
A long straight wire carries a current and produces a magnetic field. At a distance of 2 cm from the wire, the field is 4 × 10⁻⁵ T. What is the current in the wire? (μ₀ = 4π × 10⁻⁷ T·m/A)
Answer: A
B = μ₀I/(2πr). So I = 2πrB/μ₀ = 2π × 0.02 × 4 × 10⁻⁵/(4π × 10⁻⁷) = 2 A.
Q.199Medium
A beam of electrons is accelerated through a potential difference V and then enters a region of perpendicular electric and magnetic fields. For the electrons to move undeflected, which condition must be satisfied?
Answer: B
For undeflected motion, electric force equals magnetic force: qE = qvB, which simplifies to E = vB. This is the velocity selector condition.
Q.200Medium
A conducting rod of length L = 0.5 m moves with velocity v = 10 m/s perpendicular to a uniform magnetic field B = 2 T. The motional EMF induced is:
