Relative phase between resistor and capacitor voltages in series RC In any series RC circuit at a single frequency, what is the phase difference between the voltage across the capacitor and the voltage across the resistor?

Introduction / Context:Although the overall source-to-current phase in a series RC depends on component values and frequency, the voltages across the individual elements have a fixed quadrature relationship. Recognizing this helps in phasor diagram construction and in diagnosing measurement results on oscilloscopes.

Given Data / Assumptions:

• Topology: series RC.
• Sinusoidal steady-state.
• Ideal components.
• We compare only VR (across R) with VC (across C).

Concept / Approach:In series RC, the current I is common to both elements. The resistor voltage is in phase with I: VR = I * R (0° relative to I). The capacitor voltage lags the current by 90°: VC = I * (−j|XC|). Therefore, VC lags VR by 90° regardless of magnitude, making their phase difference fixed at 90°.

Step-by-Step Solution:

Verification / Alternative check:Draw the phasor diagram: place VR along the positive real axis and VC along the negative imaginary axis. The right angle between them is evident. This geometric proof does not depend on values of R or C.

Why Other Options Are Wrong:

Common Pitfalls:Confusing the fixed VR–VC phase with the variable source-to-current phase; mis-assigning lead/lag directions.

Final Answer:equals 90°