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?
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Adepends on the values of R and C
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Bequals 0°
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Cequals 90°
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Ddepends on the value of the input voltage
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Eequals 45° at all frequencies
Answer
Correct Answer: equals 90°
Explanation
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:
Reference current I at 0°.VR is aligned with I (0°).VC is −90° relative to I.Hence, phase(VC) − phase(VR) = −90°, magnitude of difference = 90°.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:
depends on R and C: incorrect for the inter-element voltage relationship.equals 0° / 45°: contradicts capacitor voltage’s inherent 90° lag to current.depends on input voltage amplitude: phase in linear passive networks is amplitude independent.Common Pitfalls:Confusing the fixed VR–VC phase with the variable source-to-current phase; mis-assigning lead/lag directions.
Final Answer:equals 90°