Question

: Two coils of self-inductance \[100\;{\rm{mH}}\] and \[400\;{\rm{mH}}\] are placed very close to each other. Find the maximum mutual inductance between the two when \[4\;{\rm{A}}\] current passes through them: -
1. \[200\;{\rm{mH}}\]
2. \[300\;{\rm{mH}}\]
3. \[100\sqrt 2 \;{\rm{mH}}\]
D. None of these

Answer 1

Hint: The above problem can be resolved using the mathematical expression for the maximum value of mutual inductance. The self-inductance is that property of coil, by which there is the subsequent generation of the magnetic flux due to the induced emf, within the same coil. On the other hand, the mutual inductance has occurred, when there is variation in the magnetic flux by any other coil. In this problem, we are given with values of self-inductance of two coils, such that some magnitude of the current is flowing across coils. Then we need to substitute the numerical values in the formula to obtain the final result.

Complete step by step answer:
Given:
The self- inductance of one coil is, \[{L_1} = 100\;{\rm{mH}}\].
The self- inductance of another coil is, \[{L_2} = 400\;{\rm{mH}}\].
The magnitude of current is, \[I = 4\;{\rm{A}}\].
The expression for the maximum mutual inductance is,
\[M = \sqrt {{L_1} \times {L_2}} \]
Solve by substituting the values in the above equation as,
\[
M = \sqrt {{L_1} \times {L_2}} \\
M = \sqrt {100\;{\rm{mH}} \times 400\;{\rm{mH}}} \\
M = 200\;{\rm{mH}}
\]
Therefore, the magnitude of maximum mutual inductance is \[200\;{\rm{mH}}\].

Note:To solve the given problem, one must understand the concept and applications of mutual induction as well as self-induction. The mutual induction can occur when there are some magnetic flux changes in one coil, but its effect can be seen on another coil. On the other hand, it is also important to remember the significance of self-induction along with its relation with mutual induction. The mathematical formulation involves the mutual inductance equivalent to the product of the square root of the self-inductance.