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Mutual Inductance, Mutual Inductance for two coaxial long solenoids, Mutual Inductance for a pair of concentric coils is considered one of the most asked concept.
18 Questions around this concept.
The flux linked with the secondary coil due to current
What will be mutual inductance if there is no current flowing in the primary coil(Open Circuit)?
What will be mutual inductance if current I is flowing in primary coil? (Coefficient of coupling K=0)
What will be the inductance of the secondary coil if mutual inductance is 0. (Coefficient of cooling is K).
Two coils, X and Y, are kept in close vicinity of each other. When a varying current, I(t), flows through coil X, the induced emf (V(t)) in coil Y, varies in the manner shown here. The variation of I(t), with time, can then be represented by the graph labeled as graph:
A rectangular loop of sides ‘ a ‘ and ‘ b ‘ is placed in xy plane. A very long wire is also placed in xy plane such that side of length ‘ a ‘ of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is ‘ d ‘. The mutual inductance of this system is proportional to :
A time varying current
Find the emf induced (max) (in mV ) is secondary coil of 400 turns
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An e.m.f. of 5 millivolt is induced in a coil when in a nearby placed another coil, the current changes by 5 ampere in 0.1 second. The coefficient of mutual induction between the two coils will be :
The coefficient of mutual inductance of the two coils is 0.5 H. If the current is increased from 2A to 3 A in 0.01 sec. in one of them, then the induced e.m.f. in the second coil is :
The coefficient of mutual inductance of the two coils is 0.5 H. If the current is increased from 2 to 3 A in 0.01 sec. in one of them, then the induced e.m.f. in the second coil is :
Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighboring coil or circuit will also change. Hence an emf will be induced in the neighboring coil or circuit. This phenomenon is called ‘mutual induction’.
or The phenomenon of producing an induced emf in a coil due to the change in current in the other coil is known as mutual induction.
Coefficient of mutual induction (M)-
If two coils (P-primary coil or coil 1, S-secondary coil or coil 2) are arranged as shown in the below figure.
If we change the current through the coil P (i.e
where
Similarly, if we exchange the position of Coil 1 and Coil 2
then
If we change the current through the coil S (i.e
where
- As
If
I.e coefficient of mutual induction of two coils is numerically equal to the magnetic flux linked with one coil when unit current flows through the neighboring coil.
- Using Faraday's Second Law of Induction emf we get
If
I.e The coefficient of mutual induction of two coils is numerically equal to the emf induced in one coil when the rate of change of current through the other coil is unity.
Units and dimensional formula of '
S.I. Unit - Henry (H)
And
And its dimensional formula is
Dependence of mutual inductance
- Number of turns
- Coefficient of self inductances
and the relation between
where
If
If
- Distance(d) between two coils (i.e As dincreases then M decreases)
- The magnetic permeability of medium between the coils
Consider two long co-axial solenoids of the same length l..Let A1 and A2 be the area of cross-section of the solenoids with A1 being greater than A2 as shown in the below figure.
The turn density of these solenoids are
Let
As the field lines of
So the magnetic flux linked with each turn of solenoid 2 due to solenoid 1 and is given by
The total flux linkage of solenoid 2 with total turns
And Using
Where
Similarly
Hence
So, In general, the mutual inductance between two long co-axial solenoids is given by
If a dielectric medium of permeability
Consider two circular coils one of radius 'r1' and the other of radius' r2'placed coaxially with their centers coinciding as shown in the below figure.
Since so we can assume coil 2 is at the center of coil 1.
If
Suppose a current flows through the outer circular coil.
Then Magnetic field at the center of the coil 1 is given as
So the total flux passing through coil 2 will be given as
And using
we get
Where M=mutual inductance between two concentric coils
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