Test: Inductance (17 Dec) - JEE MCQ

Now, e=L(di/dt)
L=e/(di/dt)
1 henry=1 volt/(1 ampere/second)

Coefficient of mutual induction:-
It is a measure of the induction between two circuits, It is the ratio of the electromotive force in a circuit to the corresponding change of current in neighboring circuits; usually measured in henries.
Coefficient of mutual induction is the ratio of induced e.m.f in secondary coil to the rate of change of current in primary coil.

E = CV²/2

= 9.2 x (22.5)²/2

= 2328.75 J

n₁=10 turns per cm, =1000 turns per metre
n₂l=100, A=10 c=0.1 m², M=μ₀n₁(n₂l) A
=4πx10^-7×1000×100×0.1H=0.13mh

Inductance in electric circuits plays the same role as moment of inertia in mechanical circuits.

The total inductance of inductors connected in series is given by the following formula:
L_eq = L₁ + L₂
Substituting the values in the equation, we get the total inductance as
L_eq = L + L = 2L
Hence, the total inductance of two inductors connected in series is 2L.

The magnetic field through the secondary of N2 turns of each other of area S is given as,
N2= Φ2=N2(BS)
     =μ₀n₁N₂i₁S
M= N₂Φ₂/i1
M= μ₀n₁N₂S
Substituting the values.
M=(4πx10^-7) x100x200x5x10^-3
   =1287142.86x10^-10
   =12.57x10^-5H

As φ =mi
now take change in flux
dφ/dt=d(mi)/dt
we can write it as
dφ/ dt= m Δi/Δt
-e=m(2-5)/0.03
e=3m/0.03
1000=300m/3
m=10

Mutual inductance is the phenomena where an adjoining wire coil induces the voltage from the magnetic field produced by a wire coil. A transformer is a tool which is made up of two or more coils in close proximity to each other to create a situation of mutual inductance between the coils.The factors determining the value of mutual inductance are —
a. The number of turns of the coils
b. The geometric shape and size of the coils
c. The separation of the coils and
d. The angular orientation between the coils
So clearly it does not depend upon the current flow through both of the cells.

It is also called the Coefficient of induction. Coefficient of induction is about the ratio of current induced with respect to magnetic flux. This constant of proportionality is known as Inductance. It is a scalar quantity.
The dimension of inductance- M¹·L²·T⁻²·A⁻²