Kerala Engineering Entrance 2008 Questions on Electromagnetic Induction

Questions involving electromagnetic induction at your level are usually simple and interesting. Here are the two questions which appeared in Kerala Engineering Entrance 2008 question paper:

(1) If the self inductance of 500 turn coil is 125 mH, then the self inductance of similar coil of 800 turns is

(a) 48.8 mH

(b) 200 mH

(c) 187.5 mH

(d) 320 mH

(e) 78.1 mH

Self inductance is the total magnetic flux linked with the coil when unit current flows through the coil. Since the total flux and the magnetic field are directly proportional to the number of turns in the coil, the self inductance is directly proportional to the square of the number of turns in the coil. Therefore we have

500²/800² = 125/L where L is the self inductance of the 800 turn coil.

This yields L = 320 mH.

(2) The flux linked with a circuit is given by Φ= t³ + 3t – 7. The graph between time (x–axis) and induced emf (y–axis) will be a

(a) straight line through the origin

(b) straight line with positive intercept

(c) straight line with negative intercept

(d) parabola through the origin

(e) parabola not through the origin

The induced emf, V = – dΦ/dt = – 3t² – 3

If V is plotted against t, a parabola which does not pass through the origin will be obtained. So the correct option is (e).

Here are two questions on self inductance:

(1) The inductance between A and D is
(a) 3.66 H (b) 9 H (c) 0.66 H (d) 1 H

This question appeared in AIEEE 2002 question paper. If you examine the arrangement carefully, you will realise that the three iductors, each having value 3 henry are connected in parallel, between the points A and D.
Inductors connected in parallel will produce an effective value given by the reciprocal relation,
1/L = 1/L₁ + 1/L₂ + 1/L₃.
Since all the three inductors have the same value 3H, the effective value of the inductance is 3H/3 = 1 H
[If the three components were capacitors of value 3 μF each, the effective value would be 9 μF because capacitances in parallel get added as C = C₁ + C₂ + C₃ + etc. It will be convenient to remember that Resistors, reactances ( inductive as well as capacitive) and impedances get added when connected in series ( Z = Z₁ + Z₂ + Z₃ + etc.) while their effective value is given by the reciprocal relation when they are connected in parallel (1/Z = 1/Z₁ + 1/Z₂ + 1/Z₃ +…etc.)].

(2) An air cored coil of 600 turns has a self inductance of 90 mH. If the number of turns is reduced to 200 without changing the area of the coil, the self inductance will be
(a) 30 mH (b) 270 mH (c) 180 mH (d) 90 mH (e) 10 mH

The answer to this question is 10 mH since the self inductance of a coil is directly proportional to the square of the numbr of turns. When the number of turns becomes one third, the inductance becomes one nineth.
[The self inductance is equal to the total magnetic flux linked with the coil (because of its own magnetic field) when unit current flows in it. But this magnetic flux is directly proportional to the magnetic field produced by the coil and the total number of turns in the coil. Since the magnetic field produced by the coil is directly proportional to the total number of turns in the coil, the total magnetic flux linked (and hence the self inductance) is directly proportional to the square of the number of turns in the coil]