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Two coupled inductors L 1 = 8H and L 2 = 32H have coefficient of coupling K = 0.4. The mutual inductance between them is
40 H
102.4 H
64 H
6.4 H
6.4 H
The mutual inductance M between two magnetically coupled inductors is calculated using the product of their self-inductances and the coefficient of coupling K. Given L1тАЛ=8┬аH, L2тАЛ=32┬аH, and K=0.4, the mutual inductance is M=KL1тАЛL2тАЛтАЛ=0.48├Ч32тАЛ=0.4├Ч256тАЛ=0.4├Ч16=6.4┬аH.
IS 1885 (Part 33): Electrotechnical Vocabulary - Transformers and Inductors
The mutual inductance M between two magnetically coupled inductors is calculated using the product of their self-inductances and the coefficient of coupling K. Given L1тАЛ=8┬аH, L2тАЛ=32┬аH, and K=0.4, the mutual inductance is M=KL1тАЛL2тАЛтАЛ=0.48├Ч32тАЛ=0.4├Ч256тАЛ=0.4├Ч16=6.4┬аH.
M=KL1тАЛL2тАЛтАЛ тАФ Definition of mutual inductance where M is in Henry (H), K is the dimensionless coefficient of coupling, and L1тАЛ,L2тАЛ are self-inductances in Henry (H).
Magnetic coupling occurs when the magnetic flux produced by one coil links with the turns of another coil. The degree of this flux linkage is defined by the coefficient of coupling K, which ranges from 0 (no coupling) to 1 (perfect coupling).
Mutual inductance M represents the ability of one inductor to induce a voltage in another due to a change in current in the first.
The maximum possible value of M is L1тАЛL2тАЛтАЛ (when K=1).
Coupling coefficient K is independent of the number of turns but depends on geometry and magnetic core permeability.
Fundamental principle behind transformer operation.
Essential for impedance matching in resonant circuits.
Unwanted mutual coupling causes electromagnetic interference (EMI) in sensitive electronic circuits.
Magnetic leakage reduces the efficiency of energy transfer.
Transformers
Wireless power transfer systems
Option A (40 H) likely results from incorrectly multiplying L1тАЛ+L2тАЛ by K.
Option B (102.4 H) is a calculation error involving incorrect root extraction.
Option C (64 H) ignores the coefficient of coupling K and calculates L1тАЛL2тАЛтАЛ only.
D is correct тАФ The calculation M=0.4├Ч8├Ч32тАЛ yields exactly 6.4 H.
Always ensure K is between 0 and 1. If K is not given, assume ideal coupling (K=1) for transformers unless stated otherwise.
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