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
(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.)].
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
(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]
[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]
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