Series combination of capacitive reactances — qualitative effect on total Xc When capacitive reactances are connected in series, what happens to the total capacitive reactance of the combination?

Introduction / Context:
Knowing how reactances combine helps anticipate impedance and voltage distribution in AC networks. For series networks, impedances simply add as complex quantities.

Given Data / Assumptions:

• Two or more capacitive reactances Xc1, Xc2, ... connected in series.
• Sinusoidal steady-state analysis.
• Ideal linear elements.

Concept / Approach:
Impedances in series add: Z_total = Σ Zi. For purely capacitive branches, Zi = -jXci. Thus Xc,total = Xc1 + Xc2 + ... . Adding positive magnitudes yields a larger total reactance magnitude, meaning greater opposition to AC current.

Step-by-Step Solution:
Write each branch impedance: Zi = -jXci.Series sum: Z_total = -j(Xc1 + Xc2 + ...).Magnitude increases with each additional series reactance: |Z_total| = Xc1 + Xc2 + ... .Therefore, the total capacitive reactance increases when connected in series.

Verification / Alternative check:
Duality with resistors: resistances in series also add. In contrast, capacitors themselves (as components) in series reduce equivalent capacitance, but their individual reactances at a given frequency still add.

Why Other Options Are Wrong:

• Decrease or no change: contradicts series impedance addition.
• “Total opposition to voltage”: imprecise; reactance describes opposition to AC current at a given frequency.

Common Pitfalls:

• Mixing up capacitor combination rules (for C values) with reactance combination (for Xc values).
• Forgetting frequency dependence; Xc changes with f even if component values are fixed.

Final Answer:
an increase in total XC