Relationship Between Mutual and Self-Inductance – Rankers Physics
Topic: Electromagnetic Induction
Subtopic: Mutual Induction

Relationship Between Mutual and Self-Inductance

Assertion (A): A system cannot have mutual inductance without having self inductance.
Reason (R): If mutual inductance of system is zero, its self-inductance must be zero.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true, as mutual inductance \(M\) depends on the self-inductances \(L_1\) and \(L_2\) (\(M \le \sqrt{L_1 L_2}\)). Reason (R) is false; if two coils are perfectly uncoupled (\(k=0\)), their mutual inductance is zero, but their self-inductances \(L_1\) and \(L_2\) can still be non-zero.

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