Inductive reactance of a series–parallel inductor network: Two 10 H inductors are connected in parallel, and this parallel combination is then in series with a third 10 H inductor. What is the approximate total reactance at 7 kHz?

Introduction / Context:Series–parallel combinations of inductors reduce to an equivalent inductance that determines the overall reactance X_L = 2π f L_eq. Accurate reduction and unit conversion are core skills for AC network analysis at audio and RF frequencies.

Given Data / Assumptions:

• L1 = 10 H in parallel with L2 = 10 H.
• That parallel pair is in series with L3 = 10 H.
• Frequency f = 7 kHz; ideal inductors (no resistance considered).

Concept / Approach:Two equal inductors in parallel produce L_par = L/2. Then add the series inductor to get L_eq. Finally compute X_L = 2π f L_eq and convert to kilohms for comparison to options.

Step-by-Step Solution:

Verification / Alternative check:Reasonableness: A very large inductance at several kilohertz should yield hundreds of kilohms of reactance; the computed value aligns with that intuition.

Why Other Options Are Wrong:

• 66 kΩ: A factor-of-10 error from dropping a zero in the frequency or inductance.
• 219 kΩ or 1.3 MΩ: Do not match 2πfL with L_eq = 15 H at 7 kHz.

Common Pitfalls:

• Mistaking parallel of equal inductors as 2L (it is L/2).
• Dropping units when converting to kilohms.

Final Answer:660 kΩ