15 extra multiple-choice questions for Electromagnetic Induction And Alternating Current (12th Standard Physics, Samacheer Kalvi), beyond the ones printed in the textbook — each with the correct option highlighted and a clear, worked explanation. Free to read in English and Tamil.
Q1
A rectangular loop of area A is placed in a uniform magnetic field B. If the angle between the magnetic field direction and the plane of the loop is 30 degrees, what is the magnetic flux linked with the loop?
- A. BA
- B. BA / 2Correct
- C. (sqrt(3) * BA) / 2
- D. Zero
Explanation. The magnetic flux is defined as Phi = BA cos(theta), where theta is the angle between the magnetic field and the normal to the area. If the angle with the plane is 30 degrees, then the angle with the normal is 90 - 30 = 60 degrees. Therefore, Phi = BA cos(60) = BA / 2.
Q2
According to Lenz's law, the induced current in a circuit always flows in a direction such that its own magnetic field opposes:
- A. the existing magnetic flux
- B. the external magnetic field
- C. the change in magnetic fluxCorrect
- D. the electromotive force
Explanation. Lenz's law is a consequence of the law of conservation of energy, stating that the direction of induced current is such that it opposes the change in magnetic flux that produced it.
Q3
To minimize power loss due to eddy currents in the core of a transformer, the core is typically:
- A. made of a single solid block of soft iron
- B. constructed from thin, insulated laminationsCorrect
- C. cooled to cryogenic temperatures
- D. made of a non-magnetic material
Explanation. Eddy currents flow in circular paths within the conductor. By using thin laminations insulated from each other, the path for eddy currents is broken, significantly reducing energy loss as heat.
Q4
The self-inductance of a long solenoid of length l, area A, and total number of turns N in vacuum is given by:
- A. (mu_0 * N^2 * A) / lCorrect
- B. mu_0 * N * A * l
- C. (mu_0 * N * A) / l
- D. mu_0 * N^2 * A * l
Explanation. The self-inductance L of a solenoid is calculated as L = (mu_0 * n^2 * A * l), where n is the turns per unit length (n = N/l). Substituting n gives L = mu_0 * (N/l)^2 * A * l = (mu_0 * N^2 * A) / l.
Q5
Two neighboring coils have a mutual inductance of 2 H. If the current in the first coil changes at a constant rate of 5 A/s, the magnitude of the induced emf in the second coil is:
- A. 2.5 V
- B. 5 V
- C. 10 VCorrect
- D. 20 V
Explanation. The induced emf in the secondary coil is given by the formula epsilon = M * (di/dt). Here, M = 2 H and di/dt = 5 A/s, so epsilon = 2 * 5 = 10 V.
Q6
A metal rod of length L moves with a constant velocity v perpendicular to a uniform magnetic field B. The induced motional emf across its ends is:
- A. BLvCorrect
- B. 0.5 * BLv
- C. BLv^2
- D. B^2Lv
Explanation. Motional emf is produced due to the Lorentz force acting on the free electrons in the conductor. When the motion is perpendicular to the field, the induced emf is exactly equal to the product of magnetic induction, length, and velocity.
Q7
In a single-phase AC generator, the induced emf is at its maximum value when the plane of the rotating coil is:
- A. perpendicular to the magnetic field lines
- B. parallel to the magnetic field linesCorrect
- C. inclined at 45 degrees to the field lines
- D. stationary within the field
Explanation. The induced emf is given by epsilon = NBAw sin(wt). It is maximum when sin(wt) = 1 (wt = 90 degrees), which means the normal to the coil is perpendicular to the field, making the plane of the coil parallel to the field.
Q8
In an ideal step-up transformer, which of the following is true when comparing the secondary to the primary?
- A. The secondary voltage is higher and current is higher
- B. The secondary voltage is lower and current is lower
- C. The secondary voltage is higher and current is lowerCorrect
- D. The secondary voltage is lower and current is higher
Explanation. A step-up transformer increases voltage (Ns > Np). By the principle of conservation of energy (assuming 100% efficiency), the input power equals output power (VpIp = VsIs). If voltage increases, the current must decrease proportionally.
Q9
The root mean square (RMS) value of a sinusoidal alternating current with a peak value Im is:
- A. Im / 2
- B. Im / sqrt(2)Correct
- C. sqrt(2) * Im
- D. 2 * Im
Explanation. The RMS value, or effective value, is defined as the square root of the mean of the squares of the current over one cycle. For a sine wave, this mathematical average results in the peak value divided by the square root of 2.
Q10
In an AC circuit consisting of a pure inductor, the current:
- A. leads the voltage by 90 degrees
- B. lags the voltage by 90 degreesCorrect
- C. is in phase with the voltage
- D. leads the voltage by 180 degrees
Explanation. In a purely inductive circuit, the self-induced back emf opposes the change in current. This causes the current to reach its peak value exactly one-quarter cycle (90 degrees or pi/2 radians) after the voltage reaches its peak.
Q11
If the frequency of the AC source in a purely capacitive circuit is tripled, the capacitive reactance Xc becomes:
- A. three times its original value
- B. nine times its original value
- C. one-third of its original valueCorrect
- D. unchanged
Explanation. Capacitive reactance is inversely proportional to frequency (Xc = 1 / (2 * pi * f * C)). If the frequency f is tripled, Xc will be divided by 3.
Q12
In a series RLC circuit, electrical resonance occurs when the frequency of the source is such that:
- A. The resistance is zero
- B. Inductive reactance is equal to capacitive reactanceCorrect
- C. The impedance is at its maximum value
- D. The current is at its minimum value
Explanation. Resonance happens when the frequency of the applied AC source matches the natural frequency of the circuit. At this point, XL = Xc, their effects cancel out, and the circuit's impedance Z is at its minimum (equal to R), allowing maximum current.
Q13
The power factor of an AC circuit is defined as the cosine of the phase angle between voltage and current. In a series RLC circuit, it is equal to the ratio of:
- A. Resistance to Impedance (R/Z)Correct
- B. Reactance to Resistance (X/R)
- C. Voltage to Current (V/I)
- D. Inductance to Capacitance (L/C)
Explanation. From the impedance triangle, the cosine of the phase angle phi is the adjacent side (Resistance R) divided by the hypotenuse (Impedance Z). Thus, power factor cos(phi) = R/Z.
Q14
What is the expression for the natural angular frequency of free oscillations in an LC circuit?
- A. sqrt(L * C)
- B. L * C
- C. 1 / sqrt(L * C)Correct
- D. 1 / (L * C)
Explanation. In an LC circuit, energy oscillates between the electric field of the capacitor and the magnetic field of the inductor. The natural angular frequency w at which this occurs is given by 1 divided by the square root of the product of inductance and capacitance.
Q15
A 'wattless current' occurs in an AC circuit when the phase difference between voltage and current is:
- A. 0 degrees
- B. 45 degrees
- C. 90 degreesCorrect
- D. 180 degrees
Explanation. Average power is given by P = V_rms * I_rms * cos(phi). If phi is 90 degrees, cos(90) = 0, meaning no power is consumed despite current flowing. This component of current is called wattless current, typically found in purely inductive or capacitive circuits.
