Condition for series resonance is

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I_C=I_Lsin∅_L

Explanation: In a parallel RLC circuit, resonance occurs when the circuit behaves as a pure resistance, meaning the total susceptance is zero. This implies the reactive component of the branch currents must cancel each other out, specifically requiring the imaginary part of the inductor current ($I_L sin\phi_L$) to equal the capacitor current ($I_C$). Working Principle: At resonance in a parallel circuit, the inductive susceptance ($B_L = \frac{1}{\omega L}$) is neutralized by the capacitive susceptance ($B_C = \omega C$). Since the inductive branch has both real and imaginary components, the reactive current drawn by the inductor ($I_L sin\phi_L$) must be exactly compensated by the purely reactive current drawn by the capacitor ($I_C$), ensuring unity power factor. Key Formulas: $I_C = I_L \sin\phi_L$ — Condition for parallel resonance; $Y = \frac{1}{R} + j(\omega C - \frac{1}{\omega L})$ — Total admittance of parallel RLC circuit Key Points: At resonance, the circuit acts as a resistive load with unity power factor.; The total current drawn from the supply is minimum in parallel resonance.; Parallel resonance is also known as anti-resonance or current resonance.; The impedance of the circuit is maximum at the resonant frequency. Advantages: Higher impedance at resonance; Effective for filtering specific frequencies Disadvantages: Requires precise component values; High sensitivity to frequency variations Applications: Tuned circuits in radio receivers; Oscillator circuits Additional Info: Standard value: $Q = R \sqrt{\frac{C}{L}}$ represents the quality factor.. Option B ($I_C = I_L$) is incorrect as it ignores the phase angle of the inductive branch current.. Option D ($Z = X$) is dimensionally inconsistent and describes no standard resonance condition. Answer: A is correct — The condition $I_C = I_L \sin\phi_L$ ensures that the reactive components of the branch currents cancel out, resulting in a unity power factor. Exam Tip: Always remember that in series resonance $X_L = X_C$ (impedance is minimum), whereas in parallel resonance $B_L = B_C$ (admittance is minimum).

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