Question

M with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following values of \( \frac{I_1}{I_2} \)?

• A. \( \frac{-M}{L_2} \)
• B. \( \frac{-L_2}{M} \)
• C. \( \frac{-M}{L_1} \)
• D. \( \frac{-L_1}{M} \)

Hint:

In coupled circuits, the stored magnetic energy is minimized when the current ratio \( \frac{I_1}{I_2} \) is equal to \( \frac{-M}{L_1} \).

Answer 1

The Correct Option is C

Step 1: For coupled circuits, the magnetic energy is a function of the mutual inductance \( M \) and the inductances \( L_1 \) and \( L_2 \). The energy stored in the magnetic field of the coupled system is minimized when the current ratio \( \frac{I_1}{I_2} \) reaches a specific value determined by the system parameters.
Step 2: The energy is minimum when the current ratio is \( \frac{-M}{L_1} \), as this corresponds to the condition where the magnetic coupling is at its most efficient, minimizing the stored energy.
Thus, the correct answer is \( \frac{-M}{L_1} \).