Series RLC reactance — when both inductive reactance (XL) and capacitive reactance (XC) are present in the same series circuit, is the magnitude of total reactance equal to the sum of their magnitudes?

Introduction / Context:Understanding how reactances combine in series is essential for predicting a circuit’s impedance and phase. This question distinguishes the correct rule for combining inductive and capacitive reactances in a series path.

Given Data / Assumptions:

• Single series path containing L and C (and possibly R).
• Steady-state sinusoidal operation at angular frequency ω.

Concept / Approach:In series, reactances add algebraically: X_total = XL + (−XC). Therefore, X_total = XL − XC. The magnitude is |X_total| = |XL − XC|, not the sum of magnitudes. At resonance, XL = XC and the net reactance magnitude becomes zero (ideal case), leaving purely resistive impedance.

Step-by-Step Solution:

Verification / Alternative check:Bode/phasor diagrams show the vector subtraction along the imaginary axis, not a scalar sum of lengths.

Why Other Options Are Wrong:

Common Pitfalls:Adding magnitudes instead of algebraic quantities; forgetting that capacitive reactance is negative in phasor notation.

Final Answer:False — |X| = |XL − XC|