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QUESTION: 1

The overall inductance of two coils connected in series, with mutual inductance opposing self-inductance is L_{1}; with mutual inductance aiding self-inductance the overall inductance is L_{2}. The mutual inductance M is given by

Solution:

Let the self inductances of two coils be L'_{1 }and L'_{2} respectively.

Then, L_{1 = }L'_{1} + L'_{2} - 2M (For opposing)

and L_{2} = L'_{1} + L'_{2} + 2M (For adding)

So, L_{2} - L_{1} = 4M

or,

QUESTION: 2

In case all the flux from the current in coil-1 links with coil-2, the coefficient of coupling will be

Solution:

QUESTION: 3

In series circuit shown below, for series resonant frequency of 1 rad/s, the value of coupling coefficient K will be

Solution:

Using coupling coefficient formula, wo have

Now, for resonance,

or,

or, 15 + 12 k = 18

or, K = 3/12 = 0.25

QUESTION: 4

The equivalent inductance for the following inductive circuit is

Solution:

L_{eq} = (10 + 2 - 2) + (10 + 2 - 2)+ (10 + 2 - 2) = 30 H

QUESTION: 5

The resonant frequency of the given series circuit is

Solution:

L_{eq} = L + L + 2 M

= 2 + 2 + 2 x 1 = 6 H

QUESTION: 6

A 3 H inductor has 1000 turns. What should be the number of turns to increase the inductance to 5 H?

Solution:

We know that

or,

QUESTION: 7

What is the equivalent inductance between the terminals A and B for the circuit shown below? (Given, M = 1H)

Solution:

Due to same polarity, the effect of mutual inductance will he positive.

QUESTION: 8

Assertion (A): To determine the relative polarity of the induced voltage in the coupled coil, the coils are marked with dots.

Reason (R): One each coil, a dot is placed at the terminals which are instantaneously of the same polarity on the basis of mutual inductance alone.

Solution:

QUESTION: 9

Assertion (A): When a current changes in a circuit, the magnetic fiux linking the same circuit changes and an emf is induced in the circuit.

Reason (R): Mutual inductances is the bilateral property of the linked circuit.

Solution:

The reason for assertion is that, emf is induced due to Faraday’s law of electromagnetic induction. Reason (R) and assertion (A) are individually true.

QUESTION: 10

Match List- I (Connection) with List-ll (Equivalent inductance) and select the correct answer using the codes given below the lists:

Codes:

Solution:

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