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The overall inductance of two coils connected in series, with mutual inductance opposing selfinductance is L_{1}; with mutual inductance aiding selfinductance the overall inductance is L_{2}. The mutual inductance M is given by
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,
In case all the flux from the current in coil1 links with coil2, the coefficient of coupling will be
In series circuit shown below, for series resonant frequency of 1 rad/s, the value of coupling coefficient K will be
Using coupling coefficient formula, wo have
Now, for resonance,
or,
or, 15 + 12 k = 18
or, K = 3/12 = 0.25
The equivalent inductance for the following inductive circuit is
L_{eq} = (10 + 2  2) + (10 + 2  2)+ (10 + 2  2) = 30 H
The resonant frequency of the given series circuit is
L_{eq} = L + L + 2 M
= 2 + 2 + 2 x 1 = 6 H
A 3 H inductor has 1000 turns. What should be the number of turns to increase the inductance to 5 H?
We know that
or,
What is the equivalent inductance between the terminals A and B for the circuit shown below? (Given, M = 1H)
Due to same polarity, the effect of mutual inductance will he positive.
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.
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.
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.
Match List I (Connection) with Listll (Equivalent inductance) and select the correct answer using the codes given below the lists:
Codes:
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