Mutual Inductance MCQ Quiz in मराठी - Objective Question with Answer for Mutual Inductance - मोफत PDF डाउनलोड करा

Concept:

Series Aiding:

The equivalent inductance of series aiding connection is:

Leq = L1 + L2 + 2M

Series Opposing:

The equivalent inductance of series opposing connection is:

Leq = L1 + L2 – 2M

Calculation:

The equivalent inductance for series opposition is,

Leq = 10  + 15  - 2 M  = 20

M = 2.5 mH

The equivalent inductance for series addition is,

Leq = 10  + 15  + 2 x 2.5  = 30 mH

Important Points

The equivalent inductance of the parallel aiding connection is:

Leq = \(\frac{{{L_1}{L_2} - {M^2}}}{{{L_1} + {L_2} - 2M}}\)

The equivalent inductance of the parallel opposing connection is

Leq = \(\frac{{{L_1}{L_2} - {M^2}}}{{{L_1} + {L_2} + 2M}}\)

Concept:

For a transformer, the input impedance (Z_in) for a given load impedance (Z_L) is given by:

\({Z_{in}} = {Z_L}{\left( {\frac{{{N_1}}}{{{N_2}}}} \right)^2}\)

Where Z_in is also called the Reflected impedance since it appears as if the load impedance is reflected in the primary side.

Calculation:

\(Given\;{Z_L} = {X_c} = \frac{1}{{\omega C}}\)

Therefore the value of capacitance seen across the primary is:

\({\left( {{X_c}} \right)_{in}} = {\left( {{X_c}} \right)_L}{\left( {\frac{{{N_1}}}{{{N_2}}}} \right)^2}\)

\(Given,\;\frac{{\;{N_1}}}{{{N_2}}} = \frac{5}{2}\)

\(So,\;\frac{1}{{\omega {C_{in}}}} = \frac{1}{{\omega {C_L}}}{\left( {\frac{5}{2}} \right)^2}\)

Putting values,

\({C_{in}} = {C_L}{\left( {\frac{2}{5}} \right)^2} = 10\mu \left( {\frac{4}{{25}}} \right)\)

\( = \frac{{40\mu }}{{25}} = 1.6\mu F\)

Concept:

Mutual Inductance:

When two coils are placed close to each other, a change in current in the first coil produces a change in magnetic flux, which cuts not only the coil itself but also the second coil as well. The change in the flux induces a voltage in the second coil, this voltage is called induced voltage and the two coils are said to have a mutual inductance.

Consider a pair of coupled inductors with self-inductance L₁ and L₂, magnetically coupled through coupling coefficient k.

Input and output voltage expressions are given as

V₁ = jωL₁I₁ + jωMI₂   ...(1)

V₂ = jωL₂I₂ + jωMI₁   ...(2)

Where,

ω = 2πf

\(M = K\sqrt {{L_1}{L_2}} \)

M = Mutual inductance

L1 = Inductance of coil one

L2 = Inductance of coil two

Calculation:

In the given circuit secondary is open-circuited, so I₂ = 0 A

Given secondary voltage V₂ = 7.3 V_p-p

The output voltage expression from equation(2) is given as

V₂ = jωMI1  ....(3)

The given voltage across the 22 Ω resistor is 5 Vp-p

So primary current is calculated as I₁ = 5 / 22 A_p-p

From equation(3)

|V₂| = 2π f M I₁

7.3 = 2 × π ×  100 × 10³ × M × (5/22)

M = 51.12 μH

Concept:

• The inductor is an electrical component that is capable of storing electrical energy in the form of magnetic energy. 
•  The property of an electrical component that causes an emf to be generated by changing the current flow is known as inductance. Inductance is of two types
• Self-inductance: This is the phenomena in which change in electric current produce an electromotive force in the same circuit, and is given by

ϕ = L I 

Where ϕ  = Magnetic flux, L = Self inductance, I = Current

Mutual inductance: This is the phenomena in which change in flux linked with one circuit produce an emf in another coil and is given by

ϕ = MI

Where M = mutual inductance, ϕ  = magnetic flux, I = Current

The coupling coefficient is the ratio of mutual inductance to the maximum possible value of mutual inductance and is given by

\(K = \dfrac{M}{\sqrt{L_{1}L_{2}}}\)

Where M = Mutual inductance, L1, L2 = Self-inductance of coil 1 and coil 2 respectively

Explanation:

The maximum possible value of mutual inductance is at K = 1

M = \(\sqrt{L_1\times L_2}\)

Concept

The value of the mutual inductance is given by:

\(M={N_B\space × \spaceϕ_{BA}\over {I_A}}\)

where, M = Mutual inductance

Calculation

Given, N_B = 400

I_A = 10 A

ϕ_A = 20 mWb

60% of the flux produced by coil A links with coil B.

ϕ_BA = 0.6 × ϕ_A

ϕBA = 0.6 × 20 mWb = 12 mWb

\(M={400\space × 12\times 10^{-3}\over 10}=0.48H\)

Concept of Mutual Inductance:

Mutual inductance (M) between two magnetically coupled coils depends on several factors, such as:

• The number of turns in each coil (N₁ and N₂)
• The permeability of the core material (μ)
• The cross-sectional area of the common core (A)
• The distance and orientation between the coils (l)
  M = \(\frac{N_1N_2}{S}=\frac{\mu AN_1N_2}{l}\)

However, mutual inductance does not directly depend on the temperature of the coils. While temperature can affect the resistance of the coils and potentially the permeability of the core material to some extent, it is not a primary factor in the calculation of mutual inductance.

Concept:

Mutual Inductance

When two coils are placed close to each other, a change in current in the first coil produces a change in magnetic flux, which lines not only the coil itself but also the second coil as well. The change in the flux induced voltage in the second coil. The voltage is called induced voltage and the two coils are said to have a mutual inductance.

The coupling coefficient K represents how closely they are coupled.

We have expression 

\(M = K\sqrt {{L_1}{L_2}} \)

Where 

M = Mutual inductance

L1 = Inductance of coil one

L2 = Inductance of coil two

Calculation:

Given

L1 = 4 H

L2 = 16 H

K = 1

\(M = K\sqrt {{L_1} \times {L_2}} = 1\sqrt {4 \times 16} = 8\;H\)

For the maximum value of inductance, the value of K must be equal to 1

Concept:

Let current through the two coils are I₁ & I₂ and the voltages are V₁ & V₂ respectively.

∴ The voltage induced in the 2^nd coil due to current in the first coil can be calculated as:

\({V_2} = M\frac{{d{I_1}}}{{dt}}\)  

Where M = Mutual inductance between two inductive coils

dI₁ = change in current

dt = change in time

Calculation:

Mutual inductance (M) = 0.3

Change in current (dI₁) = 4 – 1 = 3 A

Change in time (dt) = 0.03 sec

\({V_2} = 0.3\;\left[ {\frac{{4 - 1}}{{0.03}}} \right] = 30\;V\)

Explanation:

• Mutual inductance is the phenomenon by which an induced e.m.f. is produced in a coil due to change in the electric current or the magnetic flux associated with a different, neighboring coil. ​

• The mutual induction between the two coils is affected by​
  • ​​The permeability of the core material on which the coils are wound. Mutual induction increases with the increase in magnetic permeability. ​
  • The distance between the two coils. With the increase in the distance, mutual induction decreases.
  • Shape and size of the two coils.
  • The orientation of the two coils; mutual induction is maximum when they are on the same core, less along a common axis, and minimum on a perpendicular axis.

• Mutual Inductance is the basic operating principle of the transformer, motors, generators, and any other electrical component that interacts with another magnetic field. Then we can define mutual induction as the current flowing in one coil that induces a voltage in an adjacent coil.
• But mutual inductance can also be a bad thing as “stray” or “leakage” inductance from a coil can interfere with the operation of another adjacent component by means of electromagnetic induction, so some form of electrical screening to a ground potential may be required.
• The amount of mutual inductance that links one coil to another depends very much on the relative positioning of the two coils.

Mutual Inductance between Coils is given by:

\(M=\frac{\mu_o\mu_rN_1N_2 A}{L}\)

Where:

µo is the permeability of free space (4π x 10-7)

µr is the relative permeability of the soft iron core

N1, N2 is in the number of coil turns

A is in the cross-sectional area in m2

L is the coil's length in meters.