Series RLC Circuit + Resonance
AC Circuits
44
JEE Qs
12%
Hard
75
min
Master phasor diagrams to intuitively understand phase relationships and correctly apply vector addition for voltages and currents in RLC circuits, especially during resonance conditions.
🧮 Key Formulas
✅ Key Points for JEE
- 1Phasor diagrams are indispensable for visualizing the phase relationships between voltage and current across different components and for correctly calculating the total impedance and phase angle.
- 2At series resonance (X_L = X_C), the circuit impedance is minimal (Z = R), leading to maximum current (I_rms = V_rms/R), zero phase difference (phi = 0), and unity power factor (cos(phi) = 1).
- 3The quality factor (Q) indicates the sharpness of the resonance; a higher Q implies a sharper peak in current vs. frequency graph, meaning the circuit is more selective in passing frequencies near resonance.
- 4Average power is only dissipated by the resistor (P_avg = I_rms^2 * R) in an ideal RLC circuit, as inductors and capacitors do not dissipate energy over a full AC cycle.
- 5The voltage across the inductor and capacitor can be much larger than the source voltage at resonance, even cancelling each other out due to their 180-degree phase difference.
⚠️ Common Mistakes
- ✕Adding voltages or currents algebraically instead of using phasor (vector) addition, which accounts for phase differences.
- ✕Confusing angular frequency (omega) with linear frequency (f) and using the wrong one in reactance calculations (X_L = omega L, X_C = 1/(omega C)).
- ✕Incorrectly identifying the implications of resonance (e.g., maximum current, minimum impedance, unity power factor, V_L = V_C).
- ✕Errors in calculating the phase angle, especially when X_C > X_L or misinterpreting the arctan result.
📝 Practice Questions
See allQ47.In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ ×104 radians s−1 .
Q28.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury 2025 (29 Jan Shift 1) JEE Main Previous Year Paper tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor + , where ω is frequency of the supply across resistor R and inductor L . If the choke (R/√R2 ω2L2) coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the above statements, choose the most appropriate answer from the options given below : (1) (A) is true but (R) is false (2) Both (A) and (R) are true and (R) is the correct explanation of (A) (3) (A) is false but (R) is true (4) Both (A) and (R) are true but (R) is not the correct explanation of (A)
Q39.A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0 . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be (1) 2I0 (2) I0 (3) I0 (4) I0 2 √2
Q46.A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5μ F. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ Vs−1 .
Q28.An alternating current is given by I = IA sin ωt + IB cos ωt. The r.m.s current will be ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2025 (24 Jan Shift 1) JEE Main Previous Year Paper (1) |IA+IB| (2) A+I2B √2 √I2 2 B + I2B (4) √I2A+I2 (3) √I2A 2
Q15.In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below : (1) A, B and C only (2) A and B only (3) B, C and D only (4) A, B and D only →
NCERT Chapters
- Class 12 Physics Part I Ch 7: Alternating Current