Physics

Capacitive reactance (Xc) is calculated using the formula Xc = 1 / (2πfC). Given f = 50 Hz and C = 100 µF = 100 × 10⁻⁶ F, substituting these values gives Xc = 1 / (2 × 3.1416 × 50 × 100 × 10⁻⁶) ≈ 31.83 Ω. The closest option to this value is 32 Ω, which corresponds to option A. Therefore, the correct answer is A (32 Ω).

Using both hands to turn a steering wheel creates a couple, which is a pair of equal and opposite forces whose effect is to produce rotation. This couple generates torque more effectively than a single force, making it easier to turn the wheel.

The maximum current through the galvanometer is calculated using Ohm's law: I = V / R = 100 mV / 50 Ω = 0.1 V / 50 Ω = 0.002 A = 2 mA. Therefore, the correct answer is 2.0 mA.

In an electromagnetic wave, the direction of propagation is perpendicular to both the electric and magnetic fields, which are themselves perpendicular to each other. This orthogonal relationship is fundamental to the nature of electromagnetic wave propagation.

The expression cosθ î + sinθ ĵ represents a vector of unit length pointing at an angle θ from the x-axis, which is the definition of a unit vector in that direction.

The sensitivity of a galvanometer is defined as the deflection per unit current, which is given by the formula S = BAN/C, where B is the magnetic field strength, A is the area of the coil, N is the number of turns, and C is the torsional constant of the suspension wire.

Turning a steering wheel with both hands is easier because the forces applied by the hands create a couple, producing a torque that helps rotate the wheel more effectively than a single force. This torque (couple) makes it easier to turn the wheel.

The original current is I = I₀ sin(πt), where the amplitude is I₀ and angular frequency is π. To double the amplitude and frequency, the amplitude becomes 2I₀ and angular frequency becomes 2π, so the equation is I = 2I₀ sin(2πt).

The cross product of the unit vectors $\hat{i}$ and $\hat{j}$ is $\hat{k}$. This is a fundamental property of the right-handed coordinate system in vector algebra.

Soft iron is the most suitable material for the core of an electromagnet because it has high magnetic permeability, which allows it to become strongly magnetized and enhances the magnetic field produced by the coil. Air and Cu-Ni alloy have very low magnetic permeability, and steel is harder and retains magnetism, making soft iron preferable for electromagnet cores.