Explanation:

When inductors are connected in parallel, the equivalent inductance is given by the reciprocal of the sum of the reciprocals of the individual inductances. Mathematically, we can represent it as:

1/L_eq = 1/L_1 + 1/L_2 + 1/L

Let's substitute the given values into the equation:

1/L_eq = 1/1 H + 1/2 H + 1/L H

Simplifying the equation:

1/L_eq = (2 + 1 + 1/L) / 2L

Now, to find the maximum value of the equivalent inductance, we need to find the minimum value of the denominator. This occurs when L is at its maximum value. Since L is a variable, there is no limit to its maximum value. Therefore, the minimum value of the denominator is 1/∞, which tends to zero.

Substituting the minimum value of the denominator into the equation:

1/L_eq = (2 + 1 + 0) / 2∞

Taking the reciprocal of both sides:

L_eq = 2∞ / (2 + 1)

Simplifying:

L_eq = ∞

Therefore, the maximum value of the equivalent inductance is infinity, which is not a valid physical value. Hence, the correct answer is option 'D' (none of these).

Key points:
- When inductors are connected in parallel, the equivalent inductance is given by the reciprocal of the sum of the reciprocals of the individual inductances.
- The maximum value of the equivalent inductance occurs when the denominator is minimized.
- The denominator can be minimized by taking the maximum value for the variable in the equation.
- In this case, the variable is L, and there is no limit to its maximum value.
- Therefore, the minimum value of the denominator is 1/∞, which tends to zero.
- The reciprocal of zero is infinity, which is not a valid physical value.
- Hence, the maximum value of the equivalent inductance is infinity, and the correct answer is option 'D' (none of these).