Video Lecture
Theory For Notes Making
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Objective Assignment
Q.1
Two pure inductors, each of self inductance L are connected in parallel but are well separated from each other, then the total inductance is
(a) L
(b) 2L
(c) \frac{L}{2}
(d) \frac{L}{4}
Ans : (c)
Q.2
The current through an inductor of 1 H is given by
i = 3t sin t
The voltage across the inductor of 1 H is
(a) 3 sin t + 3 cos t
(b) 3 cos t + t sin t
(c) 3 sin t – 3t cos t
(d) 3t cos t + 3 sin t
Ans : (d)
Q.3
Dimensions of self-inductance are
(a) [MLT–2 A–2]
(b) [ML2T–1 A–2]
(c) [ML2T–2 A–2]
(d) [ML2T–2 A–1]
Ans : (c)
Q.4
The minimum value of inductance which can be obtained using three inductances of values 2H, 3H and 6H is
(a) 1H (b) 1/6H (c) 1/3H (d) 1H
Ans : (a)
Q.5
The inductance of a coil in which a current of 0.1 A increasing at the rate of 0.5 A/s represents a power flow of 0.5 W is
(a) 2 H (b) 8 H (c) 20 H (d) 10 H
Ans : (d)
Subjective Assignment
Q.1
Define self-inductance of a coil. Write its S.I. units.
Q.2
Can one have an inductance without a resistance? How about a resistance with an inductance?
Q.3
A coil is wound on an iron core and looped back on itself so that the core has two sets of closely wound wires in series carrying current in opposite senses. How is its self inductance affected?
Q.4
Explain why resistance coils are usually double wound.
Q.5
How can the self-inductance of a given coil having ‘N’ number of turns, area of cross-section ‘A’ and length ‘l’ be increased ?
Q.6
A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
Ans : \displaystyle 7.5\,\times \,{{10}^{{-6}}}\,V
Q.7
What causes sparking in the switches when light is put off?
Q.8
What are the dimensions of inductance?
Q.9
The inductance of a coil is 0.25 H. Calculate its inductive reactance in a.c. of frequency 50 Hz.
Q.10
Name the physical quantity which is measured in weber \displaystyle am{{p}^{{-1}}}.
Q.11
When current in a coil changes with time, how is the back emf induced in the coil related to it?
Q.12
What is one henry?
Q.13
Write an expression for self inductance of a long solenoid.
Q.14
If a rate of change of current of \displaystyle 4A{{S}^{{-1}}} induced an emf of 20 mV in a solenoid, what is the self inductance of the solenoid ?
Q.15
Derive the expression for the self inductance of a long solenoid of cross sectional area A and length l having n turns per unit length.
Q.16
A long solenoid of length ‘l’ having N turns carries a current I. Decuce the expression for the magnetic field in the interior of the solenoid.
Q.17
Starting from the expression for the energy \displaystyle W=\frac{1}{{2L{{I}^{2}}}}, stored in a solenoid of self-inductance L to build up the current I, obtain the expression for the magnetic energy in terms of the magnetic field B, area A and length l of the solenoid having n number of turns per unit length. Hence show that the energy density is given by \displaystyle {{B}^{2}}/2{{\mu }_{0}}.
Q.18
Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.
Ans. 4 H
Q.19
An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10–3 s. How much is the average back emf induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.
Ans. \displaystyle |\varepsilon {{|}_{{av}}}\,=\,6.5\,v
Q.20
(a) Obtain the expression for the magnetic energy stored in a solenoid due to the current I flowing in it, in terms of magnetic field B, area of cross-section A and length l of the solenoid.
(b) How is this magnetic energy per unit volume compared with the electrostatic energy per unit volume stored in a parallel plate capacitor ?
Q.21
The current in a coil of self-inductance 2.0 henry is increasing according to I = 2 sin t2A. Find the amount of energy spent during the period when the current changes from 0 to 2A.
Ans. 4 J
Q.22
A plot of magnetic flux () versus current (I) is shown in the figure for two inductors A and B. Which of the two has larger value of self inductance ?
Ans. (a)
Q.23
Three inductances are connected as shown in fig. Calculate the resultant inductance.
