Reactance and susceptance equivalence — a capacitive reactance of 10 kΩ corresponds to what capacitive susceptance in siemens or microsiemens?

Introduction / Context:
Reactance and susceptance are reciprocal concepts used in impedance and admittance analysis. For capacitors, engineers often flip between series (reactance) and parallel (susceptance) viewpoints. This question checks your fluency with the reciprocal relationship for a specific numeric value.

Given Data / Assumptions:

• Capacitive reactance magnitude Xc = 10 kΩ.
• We are converting to capacitive susceptance Bc in siemens (S).
• Ideal sinusoidal steady-state conditions.

Concept / Approach:
Admittance Y is the reciprocal of impedance Z. For a purely capacitive element, the magnitude relationships simplify: |Z| = Xc and |Y| = Bc, and therefore Bc = 1 / Xc. Once Xc is given, its reciprocal yields susceptance in siemens. Converting to microsiemens helps match typical instrumentation scales.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check by dimensional reasoning: ohms and siemens are reciprocals. If Xc is large (10 kΩ), its admittance must be small (100 µS), which is consistent.

Why Other Options Are Wrong:

• 10 µS is off by a factor of 10; there is no extra factor of 10 in the reciprocal.
• 1 mS equals 1000 µS, which contradicts the reciprocal of 10 kΩ.
• Frequency is not needed here; Xc has already been provided, and Bc = 1/Xc.

Common Pitfalls:
Forgetting to convert kilo-ohms to ohms before taking the reciprocal or mixing up mS and µS.

Final Answer:
Correct — 100 µS.