Electromagnetic Induction and Alternating Currents Questions and Answers

Answer: B

The peak current is about 4.9 A.

The heating effect of an alternating current depends on its rms value. To produce three times the heat of 2.0 A DC in the same resistance:

\[ \begin{aligned} I_{rms}^{2}R &= 3(2.0)^{2}R \\ I_{rms} &= \sqrt{12} = 3.46\ \text{A} \\ I_{0} &= \sqrt{2}\,I_{rms} = 4.9\ \text{A} \end{aligned} \]

3.46 A is the rms value, not the peak asked for. 2.45 A and 2.0 A would produce less than three times the heat.

Answer: A

The AC supply in India is at 50 cycles per second (50 Hz).

India's grid, like that of most of Europe, Asia and Africa, runs at 50 Hz with a domestic voltage of 220-230 V.

60 Hz is used in the Americas and parts of Japan and some other countries. 100 and 120 cycles per second are double those values, the ripple frequency of rectified AC, not the supply frequency.

Answer: D

At resonance the voltage across L equals the voltage across C.

Resonance occurs when the inductive and capacitive reactances are equal, X_L = X_C. The same current flows through both, so the voltages across them are equal in size; they are 180° out of phase and cancel, leaving only the resistance.

That makes the impedance a minimum (Z = R), the current a maximum, and the power factor 1, not zero. So the other three options state the opposite of what happens.

Answer: B

The induced current opposes the change in flux.

Lenz's law states that the direction of an induced current is such that its magnetic field opposes the change in magnetic flux that produced it. If the flux through a coil is increasing, the induced current makes a field against it; if decreasing, a field that tries to maintain it. This is the reason for the minus sign in Faraday's law and follows from conservation of energy.

It does not oppose the magnetic field itself, which may be steady with no current induced, nor the applied voltage or the resistance.

Answer: A

The current leads the voltage by 90°.

In a capacitor the current is proportional to the rate of change of voltage, i = C dV/dt. For a sinusoidal voltage V₀ sin ωt the current is ωCV₀ cos ωt, which reaches its peak a quarter-cycle, or 90°, before the voltage.

A phase difference of 0° belongs to a purely resistive circuit, 180° to no single element, and 45° to a circuit where resistance and reactance are equal. (In a pure inductor the current lags by 90°.)