For RC series circuit, impedance is given by

Question

Examoogle · Accepted Answer

Option C: $Z=\sqrt{R^2 + X_C^2}$

Explanation & Concepts:
In an RC series circuit, the total opposition to current flow, known as impedance (Z), is the vector sum of resistance (R) and capacitive reactance (X_C). Because resistance and capacitive reactance are 90 degrees out of phase, the impedance is determined using the Pythagorean theorem.

Working Principle: In an RC series circuit, the voltage across the resistor is in phase with the current, while the voltage across the capacitor lags the current by 90°. The total voltage is the phasor sum: V = \sqrt{V_R^2 + V_C^2}. Dividing by current (I) yields the impedance triangle, resulting in Z = \sqrt{R^2 + X_C^2}.

Key Formulas: $X_C = \frac{1}{2\pi f C}$ — Capacitive reactance where f is frequency in Hz and C is capacitance in Farads; $Z = \sqrt{R^2 + X_C^2}$ — Impedance formula for RC series circuit in Ohms (\Omega); $\phi = 	an^{-1}(\frac{X_C}{R})$ — Phase angle calculation

Key Points: Resistance (R) provides opposition to current independent of frequency.; Capacitive reactance (X_C) is inversely proportional to frequency.; Impedance (Z) is a complex quantity represented as Z = R - jX_C.; The current leads the voltage in an RC series circuit by an angle between 0° and 90°.

Advantages: Used in high-pass and low-pass filter designs.; Simple to analyze using phasor diagrams.

Disadvantages: Power factor is always leading.; Impedance varies significantly with input frequency.

Applications: Audio tone control circuits.; Coupling and decoupling capacitors in amplifier stages.

Additional Info: The SI unit of impedance is the Ohm (\Omega).. Option A (Z=R) is true only for purely resistive circuits. Option B (Z=\sqrt{R^2 + X_L^2}) is for RL series circuits. Option D (Z=0) is physically impossible for passive circuits containing resistance.

Answer: C is correct — The impedance of an RC series circuit is the phasor sum of resistance and capacitive reactance, calculated as $Z = \sqrt{R^2 + X_C^2}$.

Exam Tip: Always remember that in series AC circuits, components are added vectorially because of the 90° phase difference between resistive and reactive voltage drops.

Examoogle · Answer

Option A: $Z=R$

Examoogle · Answer

Option B: $Z=\sqrt{R^2 + X_L^2}$

Examoogle · Answer

Option D: $Z=0$

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