Series LCR Resonance & Q-factor — Practice Questions

Free NEET Physics multiple-choice questions on Series LCR Resonance & Q-factor. Attempt each question and reveal the answer with a full explanation.

The power factor of a series LCR circuit at resonance is: 1 0 0.5 In an AC circuit, the power factor is maximum when the circuit contains: Only resistance Only inductance Only capacitance Inductance and capacitance A series LCR circuit with R = 20 , L = 1.5 H and C = 35 F is connected to a variable-frequency 200 V AC supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle? 2000 W 1000 W 500 W 4000 W The Q-factor of a resonant LCR circuit is a measure of: Sharpness of resonance Average power loss Impedance at resonance Phase difference In an LCR series circuit, the resonance frequency is f . If the inductance is doubled and the capacitance is halved, the new resonance frequency will be: f 2f f/2 f/4 In a series LCR circuit, the potential differences across L, C and R are 60 V, 20 V and 30 V respectively. The total potential difference of the source is: 50 V 110 V 70 V 10 V In a series LCR circuit, the frequency of the AC source is varied. At resonance, the phase difference between the current and the source voltage is: Zero /2 /4 The unit of the quantity LC is equivalent to the unit of: Time Frequency Velocity Capacitance In a series LCR circuit, the voltage across the inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is: 0 30 45 90 The ratio of inductive reactance to capacitive reactance in an AC circuit is 1 . This condition implies: Resonance Maximum impedance Minimum current Zero power factor In a series LCR circuit, if L is increased and C is decreased such that the product LC remains constant, the resonant frequency will: Remain unchanged Increase Decrease First increase then decrease The impedance of a series LCR circuit is minimum at: Resonance frequency Very high frequency Zero frequency Twice the resonance frequency The phase difference between the current and the voltage in a series LCR circuit at resonance is: 0 / 4 / 2 In a series LCR circuit, the resonance frequency is f 0 . If the resistance R is doubled, the new resonance frequency will be: f 0 2f 0 f 0 / 2 f 0 / 2 The bandwidth of a series LCR circuit is 200 rad/s and the resonance frequency is 1000 rad/s. The quality factor Q of the circuit is: 5 0.2 200000 20 In a series LR circuit, the inductive reactance is equal to the resistance R . The phase difference between the voltage and the current is: /4 /2 0 /6 The value of the quality factor Q is given by which of the following expressions? 1 R L C 1 L R C R C L LCR In a series LCR circuit, if the voltage of the source is V = V 0 t , the peak current at resonance is: V 0 / R V 0 / R 2 + ( L) 2 V 0 / ( L - 1/ C) Zero In a series LCR circuit, the voltage across the resistance, inductance, and capacitance are V R = 30 V, V L = 60 V, and V C = 20 V respectively. The RMS voltage of the AC source is: 50 V 110 V 70 V 40 V If the resonance frequency of a series LCR circuit is f 0 , and the inductance is doubled while the capacitance is halved, the new resonance frequency will be: f 0 2f 0 f 0 / 2 f 0 / 4 In an LCR series circuit, the voltage across each of the components L, C and R is 50 V. The voltage across the LC combination will be: 0 V 50 V 50 2 V 100 V A series LCR circuit has L = 0.01 H, R = 10 and C = 1 F. The Quality factor Q of the circuit is: 10 100 1 1000 In a series LCR circuit, the voltage across the resistor is 120 V, across the inductor is 160 V, and across the capacitor is 70 V. The power factor of the circuit is: 0.8 0.6 0.5 1.0 An inductor L and a capacitor C are connected in an LC circuit. If the initial charge on the capacitor is Q 0 , the maximum current in the circuit is: Q 0 LC Q 0 LC Q 0 LC Q 0 L C In a series LCR circuit, the voltage across R, L, C are V R, V L, V C respectively. The phase difference between the applied voltage and the current is given by: = V L - V C V R = V L + V C V R = V R V L - V C = V L - V C V R The bandwidth of a series LCR circuit is given by: R/L L/R R/C 1/ LC In an LC oscillation circuit, the maximum charge on the capacitor is Q . When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor is: Q/ 2 Q/2 Q/4 Q/ 3 The power factor of a series LCR circuit at the half-power frequencies is: 1/ 2 1/2 1 3 /2 In a series LCR circuit, at resonance, the value of the quality factor Q is 100 . If the value of inductance L is doubled and capacitance C is halved, the new Q factor will be: 200 100 50 400 In a series LCR circuit, the voltage across R is 100 V and R = 1000 . If the resonance frequency is 200 rad/s, and at resonance, the voltage across the inductor is 200 V, the value of L is: 10 H 1 H 2 H 5 H In a series LCR circuit, if the resonance frequency is f 0 , the current I in the circuit at frequency f < f 0 will: Lead the voltage Lag the voltage Be in phase with the voltage Be zero In an LC circuit, the maximum charge on the capacitor is Q . The energy is stored entirely in the electric field. When the charge becomes Q/2 , what fraction of the total energy is stored in the magnetic field? 3/4 1/4 1/2 2/3 In a series LCR circuit, the plot of I rms vs shows a peak. The width of this peak at half the maximum power is related to: R/L L/R 1/RC LC A capacitor of 10 F and an inductor of 1 H are joined in series. An AC voltage of 220 V is applied. At what frequency will the current in the circuit be maximum? 50.3 Hz 15.9 Hz 100 Hz 31.4 Hz In a series LCR circuit, the impedance Z is minimum at frequency f 0 . At frequency 2f 0 , the circuit is: Inductive Capacitive Resistive Purely capacitive An inductor L and a capacitor C are in an LC oscillation circuit. When the charge on the capacitor is half of its maximum value Q , the current in the inductor is: 3 2 Q 1 2 Q 3 4 Q 1 2 Q A dielectric slab is inserted between the plates of the capacitor in a resonant LCR circuit. The resonance frequency will: Decrease Increase Remain the same Become zero A series LCR circuit is connected to an alternating voltage source. When L is removed from the circuit, the phase difference between the current and the voltage is /3 . If instead C is removed from the circuit, the phase difference is again /3 . The power factor of the circuit is: 1.0 0.5 0.866 Zero In an oscillating LC circuit, the maximum charge on the capacitor is Q . When the charge on the capacitor is Q/2 , the ratio of the energy stored in the capacitor to the total energy is: 1:4 1:2 1:1 3:4 The quality factor Q of a series LCR circuit is given by 1 R L C . To make the circuit more selective (sharper resonance), one should: Decrease R and increase L Increase R and decrease L Increase C and decrease L Increase R and increase C A series LCR circuit has R=10 , L=2 mH, and C=5 F. The frequency at which the circuit becomes purely resistive is: 1592 Hz 1000 Hz 5000 Hz 318 Hz In a series LCR circuit, the voltage across the inductor is 160 V, across the capacitor is 160 V and across the resistor is 80 V. The peak value of the source voltage is: 80 2 V 80 V 160 V 160 2 V In a series LR circuit, X L = R . Now a capacitor with X C = R is added in series. The new power factor will be: 1 1/ 2 0 0.5 The quality factor Q of a series LCR circuit is increased if: R is decreased L is decreased C is increased R is increased An LCR series circuit is at resonance. If the capacitance is now changed to 4C , what should be the new value of inductance to maintain resonance at the same frequency? L/4 4L L/2 2L In a series LCR circuit, the current I is plotted against the angular frequency . The peak of the graph becomes sharper when: Resistance R is small Inductance L is small Capacitance C is large Resistance R is large A fully charged capacitor C with initial charge q 0 is connected to an inductor L at t=0 . The time at which the energy is stored equally between the electric and magnetic fields is: LC 4 LC 2 LC LC 8 In a series LCR circuit, L = 8 H, C = 0.5 F and R = 100 . The frequency at which the circuit has unity power factor is: 250 Hz 500 Hz 50 Hz 1000 Hz In a series LCR circuit, the plot of current I versus angular frequency has a peak. If the resistance R is decreased, the peak will: Become sharper and higher Become broader and lower Shift towards higher frequencies Remain unchanged In an LC oscillating circuit, the maximum charge on the capacitor is Q . The energy stored in the inductor when the charge on the capacitor is Q/ 2 is: 1/2 of the total energy 1/4 of the total energy 1/ 2 of the total energy Equal to total energy The bandwidth of a series LCR circuit is given by the expression: R/L L/R 1/ LC R/ LC An inductor L , a capacitor C and a resistor R are connected in series to an AC source V = V 0 t . If the frequency is gradually increased, the phase constant of the circuit: First decreases and then increases Increases continuously Decreases continuously First increases and then decreases An inductor of 20 mH, a capacitor of 100 F and a resistor of 50 are connected in series across a source of emf, V = 10 (314 t) . The power loss in the circuit is: 0.79 W 1.13 W 2.74 W 0.43 W In a series resonant LCR circuit, the voltage across R is 100 V and R = 1 k with C = 2 F. The resonant frequency is 200 rad/s. At resonance, the voltage across L is: 250 V 40 V 100 V 50 V In an LC circuit, the frequency of oscillation of the energy stored in the capacitor is f . The frequency of oscillation of the charge on the capacitor is: f/2 f 2f 4f A series L-R circuit is connected to an AC source of voltage V and angular frequency . The power factor of the circuit is P 1 . If a capacitor of capacitance C such that L = 1/( C) is added in series, the new power factor P 2 is: 1 P 1 0 1/P 1 In a series LCR circuit, the phase difference between the current and the voltage at the half-power frequencies is: /4 /2 0 In an LC circuit, the energy oscillates between the capacitor and the inductor. If the maximum charge on the capacitor is Q 0 , the energy stored in the inductor when the charge on the capacitor is Q 0/2 is: 3Q 0 2 / 8C Q 0 2 / 8C Q 0 2 / 4C Q 0 2 / 2C What is the phase difference between the current and voltage in a series LCR circuit at a frequency double the resonance frequency? (Assume X L = X C at resonance) -1 (1.5 Q) where Q is quality factor -1 (Q) /4 Zero The unit of L/(RC) is equivalent to: Ohm ( ) Henry (H) Farad (F) Second (s) A series LCR circuit with L = 100 mH, C = 10 F and R = 10 is connected to an AC source. The half-power frequencies are approximately: 151 Hz and 167 Hz 100 Hz and 200 Hz 159 Hz and 175 Hz 143 Hz and 159 Hz An ac voltage V=220 (2 10 3 t) Volt is applied to a series LCR circuit. Then the current amplitude in this circuit is: [Given: L=10 mH, C=25 F , R=100 ] 2.2 A 5.5 A 11.0 A 22.0 A In a series LCR circuit, the voltages across L and C are V L and V C respectively. The phase difference between V L and V C is: /2 Zero 2 In a series LCR circuit, resonance occurs at frequency f . If the capacitance is made 4 times, the new resonance frequency will be: f/2 2f f/4 4f In an LCR series circuit, R = 10 and the impedance Z = 20 . The phase difference between current and voltage is: 60 30 45 90