Which is true for series resonance?

Question

Examoogle · Accepted Answer

All of above

Explanation: In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, causing the net reactance to become zero. Consequently, the circuit behaves purely as a resistive load, leading to maximum current flow for a given voltage.

Working Principle: The mechanism relies on the frequency-dependent nature of reactive components. Inductive reactance $X_L = 2\pi fL$ increases with frequency, while capacitive reactance $X_C = \frac{1}{2\pi fC}$ decreases. At the resonant frequency $f_r$, these reactances cancel each other out, reducing the total impedance to the minimum value of $Z = R$.

Key Formulas: $X_L = X_C$ — Condition for resonance; $Z = \sqrt{R^2 + (X_L - X_C)^2} = R$ — Net impedance at resonance; $f_r = \frac{1}{2\pi\sqrt{LC}}$ — Resonant frequency formula

Key Points: At resonance, the power factor of the series RLC circuit is unity.; The impedance of the series circuit is minimum at resonance.; The current is maximum at resonance.; The voltage across the inductor and capacitor are equal in magnitude but opposite in phase.

Advantages: Maximum current amplification; High selectivity in tuning circuits

Disadvantages: High voltage stress across L and C components; Potential for circuit damage due to excessive currents if resistance is very low

Applications: Radio tuning circuits; Band-pass filters; Oscillators

Additional Info: Option A is correct because $Z = \sqrt{R^2 + (X_L - X_C)^2}$ reduces to $Z=R$ when $X_L=X_C$.. Option B represents the definition of the resonant frequency condition.. Option C is true because $I = \frac{V}{Z}$ and at resonance $Z=R$, so $I = \frac{V}{R}$.

Answer: D is correct — All listed conditions are fundamental properties of a series RLC circuit operating at its resonant frequency.

Exam Tip: Remember that in a parallel RLC circuit, resonance leads to maximum impedance and minimum current, which is the exact opposite of the series RLC case.

Related Questions

Discussion (0)