Question

The coefficient of self-inductance and the coefficient of mutual inductance have
A.)Same units but different dimensions
B.)Different units but same dimensions
C.)Different units and different dimension
D.)Same unit and same dimension

Answer 1

Hint: Define what is self-inductance and mutual inductance and how it works. Write the mathematical expressions which define the coefficient of self-inductance and coefficient of mutual inductance. From the mathematical expression we can find the units and dimensions of both of them.

Complete step by step answer:
Self-inductance is a phenomenon which can be defined as the induction of voltage in a current carrying wire when the current flowing through the same wire changes over time. This voltage or emf produced in the same circuit is also called the back emf because the direction of the produced emf is opposite to the applied voltage.
Mathematically we can express it as,

$emf=L\dfrac{di}{dt}$

Where L is the coefficient of self-inductance or simply self-inductance of the circuit.
Self-inductance L can be defined as the ratio of the back emf produced to the change in current in the circuit.

Unit of self-inductance is Henry.

Mutual inductance is a phenomenon which can be defined as the induction of voltage in a coil due to change in flow of current in an adjacent coil. When two or more coils are linked together by a common magnetic flux, they are said to have the property of mutual induction.
Mathematically we can express it as,

$emf=M\dfrac{di}{dt}$

Where M is the coefficient of mutual inductance or simply the mutual inductance.

Unit of mutual inductance is Henry.

Since, both the coefficient of self-inductance and coefficient of mutual inductance depend on the same physical quantity, their dimension will also be the same.
Dimension of the coefficient of self-inductance and coefficient of mutual inductance is $\left[ {{M}^{1}}{{L}^{2}}{{T}^{-2}}{{A}^{-2}} \right]$

So, the coefficient of self-inductance and the coefficient of mutual inductance have the same units and same dimension.
The correct option is (D)

Note: Inductance is the property of an electric circuit which produces an electromotive force because of the change in flow of current through the circuit or the conductor. Inductance is the ability of storing energy of an inductor.