Test: Magnetically Coupled Circuits- 2


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Test: Magnetically Coupled Circuits- 2 - Question 1

The overall inductance of two coils connected in series, with mutual inductance opposing self-inductance is L1; with mutual inductance aiding self-inductance the overall inductance is L2. The mutual inductance M is given by

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 1


Let the self inductances of two coils be  L'and L'2 respectively.
Then, L1 = L'1 + L'2 - 2M (For opposing)
and L2 = L'1 +  L'2  + 2M (For adding)
So, L2 - L1 = 4M
or, 

Test: Magnetically Coupled Circuits- 2 - Question 2

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

Test: Magnetically Coupled Circuits- 2 - Question 3

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

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 3

Using coupling coefficient formula, wo have

Now, for resonance,



or, 


or, 15 + 12 k = 18
or, K = 3/12 = 0.25

Test: Magnetically Coupled Circuits- 2 - Question 4

The equivalent inductance for the following inductive circuit is

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 4

Leq = (10 + 2 - 2) + (10 + 2 - 2)+ (10 + 2 - 2) = 30 H

Test: Magnetically Coupled Circuits- 2 - Question 5

The resonant frequency of the given series circuit is

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 5

Leq = L + L + 2 M
= 2 + 2 + 2 x 1 = 6 H

Test: Magnetically Coupled Circuits- 2 - Question 6

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

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 6

We know that


or, 

Test: Magnetically Coupled Circuits- 2 - Question 7

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

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 7

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

Test: Magnetically Coupled Circuits- 2 - 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.

Test: Magnetically Coupled Circuits- 2 - 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.

Detailed Solution for Test: Magnetically Coupled Circuits- 2 - Question 9

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.

Test: Magnetically Coupled Circuits- 2 - Question 10

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

Codes:

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