Physics · Alternating Current · NEET
Minimum. Since Z = square-root of (R^2 + (XL - XC)^2), and at resonance XL = XC, the reactance term becomes zero. So Z = R, which is the smallest impedance the circuit can have. Students often confuse this with a parallel LCR circuit, where impedance is maximum at resonance. For NEET, remember: SERIES resonance -> Z minimum; PARALLEL resonance -> Z maximum.
Current I = V/Z. At resonance Z is at its minimum value (Z = R), and dividing by the smallest possible number gives the largest current. So I_max = V/R. This is the key idea behind tuning a radio: at the resonant frequency the circuit draws the most current, so that station is picked up strongly.
Power factor = cos(phi) = R/Z. At resonance Z = R, so power factor = R/R = 1. This means the circuit dissipates maximum power and behaves like a pure resistor. The 2020 NEET PYQ below is built exactly on this fact.
Yes. Phase angle phi is given by tan(phi) = (XL - XC)/R. At resonance XL = XC, so tan(phi) = 0, meaning phi = 0. Voltage and current are perfectly in phase. Neither current leads nor lags.
No — this is a common trap. XL = XC means the REACTANCES are equal, so V_L = I*XL and V_C = I*XC are equal in magnitude but opposite in phase (180 degrees apart). They CANCEL each other in the phasor sum, so the NET reactive voltage is zero. Individually V_L and V_C can be large (even larger than the source voltage). Only their vector sum is zero.
The defining condition is XL = XC, i.e. omega*L = 1/(omega*C). Solving gives the resonant angular frequency omega_0 = 1/square-root(LC) and resonant frequency f_0 = 1/(2*pi*square-root(LC)). Resonance is only possible in a circuit that has BOTH an inductor and a capacitor; a pure RL or RC circuit can never resonate.
A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is pi/3. If instead C is removed from the circuit, the phase difference is again pi/3 between current and voltage. The power factor of the circuit is:
An ac voltage V = 220 sin(2 x 10^3 t) V is applied to a series LCR circuit with L = 10 mH, C = 25 microfarad, R = 100 ohm. The current amplitude in the circuit is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
XL = XC (reactances cancel), Z = R (minimum impedance), I = V/R (maximum current), phi = 0 (voltage and current in phase), and power factor = 1 (maximum power dissipation).
No. Resonance needs both L and C so that XL and XC can become equal and cancel. Without one of them there is nothing to cancel the reactance, so XL = XC can never happen.
Neither. At resonance the inductive and capacitive effects exactly cancel, so the circuit behaves purely resistive — like a simple resistor connected to the source.
f_0 = 1/(2*pi*square-root(LC)) hertz, obtained by setting XL = XC, i.e. omega*L = 1/(omega*C), which gives omega_0 = 1/square-root(LC). Notice R does not appear — resistance does not change the resonant frequency.
Because the series LCR circuit accepts (draws) maximum current at the resonant frequency due to minimum impedance. This is why it is used to select or tune a specific station in radios and TVs.
