In coil design for inductors, if the number of turns of wire is doubled while core geometry and material remain unchanged, how does the inductance value change?

Introduction / Context:
Inductance depends on coil turns, core geometry, and magnetic properties. Designers often adjust the number of turns to reach a target inductance for filters, chokes, and transformers. This question focuses on the turns dependence of inductance.

Given Data / Assumptions:

• Only the number of turns N is doubled.
• Core material, cross section, mean magnetic path length, and winding distribution remain the same.
• No saturation or frequency dependent effects are considered.

Concept / Approach:
For a typical coil, inductance is proportional to the square of the number of turns: L proportional to N^2. Therefore, if N becomes 2N, the new inductance L_new = (2N)^2 * k = 4 * N^2 * k = 4 * L_old.

Step-by-Step Solution:
Step 1: Recall the relation L proportional to N^2 for fixed core and geometry.Step 2: Substitute N_new = 2 * N.Step 3: Compute L_new = (2 * N)^2 * k = 4 * L_old.

Verification / Alternative check:
Dimensional and practical checks agree: doubling turns roughly quadruples inductance in air core solenoids and many cored coils when geometry is fixed.

Why Other Options Are Wrong:

• Half or one-fourth: These imply L proportional to 1/N or 1/N^2, which is not correct for fixed geometry.
• Twice: L increases faster than linearly with turns; it is quadratic.
• None of the above: Incorrect because four times is correct.

Common Pitfalls:
Assuming linear dependence on turns leads to underestimating inductance. Also, changing the winding layer build can change parasitic capacitance, but that does not alter the N^2 rule itself in this ideal scenario.

Final Answer:
multiplies the value of inductance by four.