Read RC Impedance: Compare Complex Magnitudes
In AC circuits, resistance and capacitive reactance combine as complex quantities. Use X_C = 1/(ω C), then compare the magnitudes of the series and parallel impedances.
Electricity questions depend on identifying charge, a conducting path and the condition that controls current or magnetic effect.
Separate charge, current and the path between them
Charge is a property · current needs a conducting path
Charge is a property; current needs a conducting path. Decide first whether the question concerns charging, resistance, current or earthing.
Series RC
The impedance magnitude is |Zₛ| = sqrt(R² + X_C²). The resistor and capacitor voltage drops are ninety degrees out of phase.
Parallel RC
Add admittances: Yₚ = 1/R + j ω C. Then |Zₚ| = 1/|Yₚ|. This is usually cleaner than trying to add impedances directly.
Use a dimensionless ratio
Express both impedances in terms of R and x before solving the given ratio condition.
OlympIQ exam lens
- ✓Convert frequency f to ω = 2 π f.
- ✓Use impedance for series and admittance for parallel.
- ✓Check the low- and high-frequency limits.
Do not add R and X_C as ordinary scalars in a series AC circuit; they are perpendicular phasors.
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