RC networks — is the total impedance set by combining resistance and capacitive reactance?

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:

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