Source voltage in series RC: In a series RC circuit, the measured rms voltages are 12 V across the resistor and 15 V across the capacitor. What is the rms source voltage supplied to the series combination?

Introduction / Context:
In a series RC circuit, resistor voltage is in phase with the current while capacitor voltage lags current by 90°. Therefore, the two rms drops are orthogonal and must be combined vectorially (Pythagorean theorem) to obtain the source rms voltage, not added arithmetically. This concept is central to phasor analysis.

Given Data / Assumptions:

• V_R(rms) = 12 V (in phase with current).
• V_C(rms) = 15 V (−90° relative to current).
• Series connection, ideal components.

Concept / Approach:
Because V_R and V_C are 90° apart, the source rms voltage is V_S = √(V_R^2 + V_C^2). This is the magnitude of the phasor sum in orthogonal coordinates (real-imaginary axes for phasors).

Step-by-Step Solution:

Verification / Alternative check:
Phasor diagram check: horizontal component 12 V (resistive), vertical component 15 V (capacitive). The hypotenuse magnitude (source) must exceed each component and is consistent at 19.2 V.

Why Other Options Are Wrong:

• 27 V: Simple arithmetic addition; incorrect due to phase difference.
• 3 V or 1.9 V: Magnitudes far too small for the given drops.

Common Pitfalls:

• Adding rms voltages directly without respecting phase angles.

Final Answer:
19.2 V