Mutual Inductance and Self-Inductance – Rankers Physics

Mutual Induction: Practice Problem & Solution

Assertion (A): The mutual inductance of two coils is doubled if the self-inductance of the primary and secondary coil is doubled. Reason (R): Mutual inductance \(M \propto \sqrt{L_1 L_2}\).  
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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Mutual Induction. Understanding the underlying formula is key to arriving at the correct answer below:

The mutual inductance is given by \(M = k \sqrt{L_1 L_2}\). If \(L_1\) and \(L_2\) are doubled, the new mutual inductance becomes \(M' = k \sqrt{(2L_1)(2L_2)} = 2k \sqrt{L_1 L_2} = 2M\). Thus, (A) is true and (R) correctly explains (A).

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