Question

There are two solenoids of same length and inductance \( L \) but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series. 1) They are connected in series with separated by large distance 2) they connected in series with one inside the other and senses of the turns coinciding 3) they are connected in series with one inside the other with senses of the turns opposite as depicted in figures 1, 2 and 3 respectively. The total inductance of the solenoids in each of the case 1, 2 and 3 are respectively

• A. 4L, 2L, 0
• B. 2L, 4L, 0
• C. 2L, 2L, 0
• D. 2L, 4L, 4L

Hint:

When solenoids are connected in series, the total inductance depends on the relative orientations of their magnetic fields.

Answer 1

The Correct Option is D

Step 1: Analyzing the total inductance.
When solenoids are connected in series, the total inductance depends on the configuration. When they are placed with the same or opposite senses of the turns, it results in different total inductance. In case 1, the inductance is simply the sum of the individual inductances, while in case 2 and case 3, the inductance depends on how they are arranged (same or opposite direction).

Step 2: Conclusion.
Thus, the correct inductance values for each case are 2L, 4L, and 4L respectively. Therefore, the correct answer is option (D).

Final Answer: \[ \boxed{\text{(D) 2L, 4L, 4L}} \]