RC networks — is the total impedance set by combining resistance and capacitive reactance?
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ATrue
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BFalse
Answer
Correct Answer: True
Explanation
Introduction / Context:This statement tests whether the learner understands that both resistance and reactance contribute to a complex impedance in RC circuits, shaping magnitude and phase together.
Given Data / Assumptions:
- Series or parallel RC configuration under sinusoidal steady-state.
- Resistor contributes real part; capacitor contributes negative imaginary part.
Concept / Approach:Impedance is a complex quantity Z = R + jX. In RC circuits, X = −1 / (ωC) (capacitive), so Z results from vector (phasor) combination of R and Xc. The magnitude |Z| and angle θ determine currents and phase shift.
Step-by-Step Solution:
Series RC: Z = R − j * (1 / (ω * C)); |Z| = sqrt( R^2 + (1 / (ω * C))^2 ).Parallel RC: Admittance Y = 1/R + j * ω * C; then Z = 1 / Y, again reflecting both R and C.Therefore, impedance is determined by combining resistance and capacitive reactance according to circuit topology.Verification / Alternative check:Measure with an LCR meter: changing frequency alters Xc and thus the measured |Z| and phase, proving that both R and C determine the net impedance.
Why Other Options Are Wrong:
- “False” would ignore the reactive contribution and predict incorrect currents, voltages, and power factor.
Common Pitfalls:Treating magnitudes algebraically without vector addition; impedance must be combined using complex arithmetic, not simple arithmetic sums of magnitudes except in special cases.
Final Answer:True