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Two inductively coupled coils have self-inductance L 1 =20H and L 2 =320H. Find the maximum possible mutual inductance between the coils.
100 H
80 H
40 H
10 H
80 H
The maximum possible mutual inductance (MmaxтАЛ) between two inductively coupled coils is achieved when the coefficient of magnetic coupling (k) is unity (k=1), implying perfect flux linkage between the coils. It is calculated using the geometric mean of the self-inductances.
The maximum possible mutual inductance (MmaxтАЛ) between two inductively coupled coils is achieved when the coefficient of magnetic coupling (k) is unity (k=1), implying perfect flux linkage between the coils. It is calculated using the geometric mean of the self-inductances.
M=kL1тАЛL2тАЛтАЛ тАФ Definition of mutual inductance
MmaxтАЛ=L1тАЛL2тАЛтАЛ тАФ Formula for maximum mutual inductance at k=1
When two coils are magnetically coupled, their mutual inductance depends on the self-inductances L1тАЛ and L2тАЛ and the coupling factor k. The magnetic coupling factor k ranges from 0 to 1. The theoretical limit of maximum mutual inductance occurs when all flux produced by one coil links the other, corresponding to k=1.
The coupling coefficient k is defined as L1тАЛL2тАЛтАЛMтАЛ, where 0тЙдkтЙд1.
For L1тАЛ=20┬аH and L2тАЛ=320┬аH, MmaxтАЛ=20├Ч320тАЛ=6400тАЛ=80┬аH.
Perfect coupling (k=1) is an ideal condition often assumed for perfectly coupled transformer windings.
Provides an upper theoretical bound for inductive coupling analysis.
Essential for evaluating the efficiency of magnetic circuits.
Real-world circuits rarely achieve k=1 due to leakage flux.
Does not account for parasitic capacitance or resistive losses.
Transformer design and analysis.
Coupled circuit network synthesis.
For k=1, M=20├Ч320тАЛ=80┬аH.
Options A, C, and D are incorrect as they do not satisfy the condition of k=1 with the given self-inductance values.
B is correct тАФ The maximum mutual inductance is calculated as 20├Ч320тАЛ=80┬аH when the coupling coefficient is unity.
Always remember that the maximum mutual inductance can never exceed the geometric mean of the two individual self-inductances.
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