When frequency increase, which quantity increase?

Question

Examoogle · Accepted Answer

$X_L$

Explanation: Inductive reactance ($X_L$) is directly proportional to the frequency of the AC supply. As the frequency ($f$) increases, the rate of change of current through the inductor increases, resulting in a higher back EMF and consequently a higher inductive reactance.

Working Principle: According to Faraday's Law of Induction, the back EMF generated in an inductor is $e = L \cdot \frac{di}{dt}$. In an AC circuit, where $i = I_{max} \sin(2\pi ft)$, the induced voltage leads the current by 90 degrees. The opposition offered to this flow is $X_L = 2\pi fL$. Thus, a higher frequency forces the inductor to oppose the current change more aggressively.

Key Formulas: $X_L = 2\pi fL$ — Inductive Reactance formula; $X_C = \frac{1}{2\pi fC}$ — Capacitive Reactance formula

Key Points: Inductive reactance ($X_L$) increases linearly with frequency ($f$).; Capacitive reactance ($X_C$) decreases inversely with frequency ($f$).; Resistance ($R$) is ideally independent of frequency in a pure resistor.; Inductors act as open circuits at high frequencies and short circuits at DC (f=0).

Advantages: Used in tuning circuits to select specific frequencies.; Essential for designing high-pass and low-pass filter networks.

Disadvantages: Inductors exhibit increased skin effect losses at very high frequencies.; Parasitic capacitance can cause real inductors to deviate from ideal behavior at high frequencies.

Applications: RF tuning circuits; Power supply filtering; Audio crossovers

Additional Info: For option B ($X_C$), the relation is $X_C = \frac{1}{2\pi fC}$, meaning it decreases as frequency increases.. Resistance ($R$) remains constant provided there are no skin effects or dielectric losses.

Answer: A is correct — Inductive reactance ($X_L$) is directly proportional to frequency, so an increase in frequency results in a linear increase in reactance.

Exam Tip: Remember 'ELI the ICE man': In an Inductor (L), voltage (E) leads current (I); in a Capacitor (C), current (I) leads voltage (E).

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