Questions: Impedance and Reactance

Question 1

At very high frequency (ω → ∞), a capacitor in an AC circuit behaves most like:

• A. An open circuit, blocking current completely
• B. A short circuit, passing current with almost no opposition
• C. A resistor whose resistance equals 1/C
• D. An inductor, since both store energy

Answer: (B)

Capacitive reactance X_C = 1/(ωC). As ω → ∞, X_C → 0, so the capacitor presents negligible opposition to current — it behaves like a short circuit. The common misconception is the opposite: students often think capacitors 'fill up and block' at high frequency. That intuition applies to DC or low frequency. At high frequency the voltage reverses before the capacitor can charge significantly, so current flows nearly unimpeded.

Question 2

In a series RLC circuit driven at the resonant frequency ω₀ = 1/√(LC), which statement correctly describes the total impedance?

• A. Impedance is zero because the inductive and capacitive reactances exactly cancel each other
• B. Impedance equals R (purely real); the inductive and capacitive reactances cancel, leaving only resistance
• C. Impedance is purely imaginary because the reactive elements dominate at resonance
• D. Impedance is at its maximum because both reactive elements reinforce each other

Answer: (B)

At resonance X_L = X_C, so the imaginary part of Z = R + j(X_L − X_C) becomes j(0) = 0, leaving Z = R — purely real. Impedance is not zero (it equals R); current amplitude is maximized (not impedance). The confusion arises from thinking that 'cancellation' means everything disappears — only the reactive parts cancel.

Question 3

Reactance and resistance both dissipate electrical energy, so a purely reactive circuit (mainly capacitors and inductors, no resistors) still consumes net power.

• T. True
• F. False

Answer: False

Reactive elements store and return energy — capacitors store energy in electric fields, inductors in magnetic fields — but on average over a complete cycle, neither dissipates net power. Real power (average power) P = ½|I|²R depends only on resistance. A purely reactive circuit has zero average power consumption. Only resistance converts electrical energy to heat.

Question 4

An inductor acts like a short circuit at DC (ω = 0) and presents increasing opposition to current as frequency rises.

• T. True
• F. False

Answer: True

Inductive reactance X_L = ωL. At DC (ω = 0), X_L = 0 — an ideal inductor is just a wire and carries current freely. As frequency increases, the rapidly changing current induces a larger back-EMF (by Faraday's law), increasing opposition. This is the opposite behavior from a capacitor: capacitors are opaque at low frequency, inductors at high frequency.

Question 5

Explain why a capacitor blocks DC but passes high-frequency AC, using the concept of reactance.

Model answer: Capacitive reactance is X_C = 1/(ωC). At DC (ω = 0), X_C is infinite — no steady current can flow because the capacitor charges to the applied voltage and stops. At high frequency, ω is large so X_C approaches zero, meaning current flows with almost no opposition.

Thinking through the physics: at DC the capacitor charges until the voltage across it equals the source voltage, at which point the electric field inside the dielectric exactly opposes further current flow. At high AC frequency, the voltage reverses direction before the capacitor can fully charge, so the capacitor is always in a transient state and never stops conducting. The mathematical expression X_C = 1/(ωC) captures this precisely: infinite opposition at zero frequency, zero opposition at infinite frequency.