When frequency increase, which quantity remain constant?

Question

Examoogle · Accepted Answer

$R$

Explanation: In an A.C. circuit, the resistance (R) of a pure resistor is independent of the supply frequency. Unlike inductive and capacitive reactances, which vary with frequency, the ohmic value of a resistor remains constant provided the physical properties of the material, such as temperature, remain unchanged.

Working Principle: The opposition to current flow in a resistor is due to electron collisions with the lattice structure of the material, which is not affected by the rate at which the supply voltage changes polarity. In contrast, reactances depend on the rate of change of magnetic flux ($d\Phi/dt$) or the charging current ($i = C \frac{dv}{dt}$), both of which are directly proportional to the supply frequency $f$.

Key Formulas: $X_L = 2\pi f L$ — Inductive Reactance; $X_C = \frac{1}{2\pi f C}$ — Capacitive Reactance; $R = \rho \frac{l}{A}$ — Resistance

Key Points: Resistance is purely dissipative and frequency-independent.; Inductive reactance ($X_L$) increases linearly with frequency.; Capacitive reactance ($X_C$) decreases inversely with frequency.; Skin effect can cause apparent resistance to increase at very high frequencies, but in ideal basic electrical theory, R is constant.

Applications: AC Circuit analysis; Filter circuit design; Impedance matching

Additional Info: Option A ($X_L$) is frequency-dependent and increases as frequency rises.. Option B ($X_C$) is frequency-dependent and decreases as frequency rises.

Answer: C is correct — Resistance (R) is a physical property of the component that does not vary with the supply frequency.

Exam Tip: Always remember that in AC circuits, only 'R' is frequency-independent; both 'L' and 'C' components behave differently depending on the signal frequency.

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