Resonance, Bandwidth & Q Factor

To reduce the resonant frequency in an L-C-R series circuit with a generator,

What is the value of inductance L for which the current is maximum in series LCR circuit with $C = 10\ \mu$F and $\omega = 1000$/s?

In a series LCR circuit, the inductance $L = 20$ mH, capacitor $C = 2\ \mu$F and resistance $R = 100$ ohm. The frequency at which resonance occurs is

The LC series resonant circuit produces a resonant frequency '$f$'. If L is tripled and 'C' is increased by 3C, the resonant frequency will be

An inductor of inductance $2\ \mu$H is connected in series with a resistance, a variable capacitor and an a.c. source of 10 kHz. The value of capacitance for which maximum current is drawn in to the circuit is $\frac{1}{x}$ F, where the value of x is (Take $\pi^2 = 10$)

A series resonant circuit consists of an inductor 'L' and capacitor 'C' which produces resonant frequency 'f'. If 'L' is increased by '2L' and 'C' is changed to '9C' the resonant frequency will be

An ac circuit contains a resistance of $1\text{ k}\Omega$, a capacitor of $0.1\ \mu\text{F}$ and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately:

A series LCR circuit with $R = 20\ \Omega,\ L = 1.6\text{ H}$ and $C = 40\ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\underline{\hspace{3em}}\ \Omega$.

In an LCR circuit at resonance, the a.c. source current is

A) maximum in a series LCR circuit only.

B) maximum in a parallel LCR circuit only.

C) maximum in both series and parallel LCR circuits.

D) minimum in both series and parallel LCR circuits.

The correct answer is

In LCR series circuit at resonance

In an LCR series circuit, at resonance,

An inductor of $0.5$ mH, a capacitor of $20\ \mu$F and resistance $20\ \Omega$ are connected in series with a $220$ V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2}$ A. The value of $x$ is

Which graph shows the correct variation of r.m.s. current '$i$' with frequency '$f$' of a.c. in case of series resonant circuit?

With gradual increase in frequency of an a.c. supply, the impedance of an LCR series circuit

In the circuit shown, the ratio of the quality factor and the band width is

(Given: band width = R/L)

A resistor of $200\ \Omega$, an inductor of self inductance $\left(\frac{2}{\pi^2}\right)$ H and a capacitor of unknown capacity are connected in series to an a.c. source of $100$ V and $50$ Hz. When the current and voltage are in phase the capacitance and the power dissipated is

A resistor of 100 $\Omega$, inductor of self inductance $\left(\frac{4}{\pi^2}\right)$ H and a capacitor of unknown capacity are connected in series to an a.c. source of 200 V and 50 Hz. When the current and voltage are in phase, the value of capacity is

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V = 5\sin(100t)$ The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor ( C) used is $\underline{\qquad}\ \mu\text{F}$.

In a discharging series L-C-R circuit, $C = 2\ \mu$F, $L = 1$ mH and $R = 10\ \Omega$. The ratio of the energies stored in the inductor and in the capacitor, when the maximum current flows in the circuit, is

Given below are the two circuits, choose the correct option.

In a series LCR circuit, the voltage across R is $100$ V, $R = 1$ K $\Omega$ and $C = 2\ \mu$F. The angular frequency $\omega$ is $200$ rad s${}^{-1}$. At resonance, the voltage across '$L$' is

In series LCR circuit C = 2 uF, L=1 mH and R= 10 $\Omega$. What is the ratio of energies stored in the capacitor and inductor when maximum current flows through circuit?

In series LCR resonant circuit, R=800 $\Omega$, C = 2 $\mu$F and voltage across resistance is 200 V. The angular frequency is 250 rad/s. At resonance the voltage across the capacitance is

In an LC circuit, angular frequency at resonance is $\omega$. The new angular frequency when inductance is made four times and capacitance is made eight times is

The frequency at resonance for the circuit is

A $20\ \Omega$ resistance, 10 mH inductance coil and $15\ \mu\text{F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made $\frac{1}{3}\text{rd}$, the resonant frequency

In a series LCR circuit, a resistor of $300\ \Omega$, 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 _________ $\times 10^{4}$ radians $\text{s}^{-1}$

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

A resistor of $5\ \Omega$, inductor of self inductance $\left(\frac{2}{\pi^2}\right)\text{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of $100\text{ V}, 50\text{ Hz}$ supply. When the voltage and current are in phase, the value of capacitance is

Figure shows the combination of inductances and capacitances. Resonant frequency of the $L - C$ circuit is

An a.c. e.m.f. of peak value $= 230\text{ V}$ and frequency 50 Hz is connected to a circuit with $R = 11.5\ \Omega,\ L = 2.5\text{ H}$ and a capacitor all in series. The value of capacitance is ' C ' for the current in the circuit to be maximum. The value of C and maximum current are respectively $(\pi^2 = 10)$.

In series LCR circuit C $= 2\ \mu\text{F},\ L = 5\text{ mH}$ and $R = 5\ \Omega$. The ratio of energy stored in the inductor to that in capacitor, when maximum current flows through the circuit is

An a.c. e.m.f. of peak value 230 V and frequency 50 Hz is connected to a circuit with $R = 11.5\ \Omega,\ L = 2.5\text{ H}$ and a capacitor all in series. The value of capacitance is ' $C$ ' for the current in the circuit to be maximum. The value of ' $C$ ' and maximum current are respectively ( $\pi^2 = 10$)

In series LCR resonant circuit, R $= 800\ \Omega,\ C = 2\ \mu\text{F}$ and voltage across resistance is 200 V. The angular frequency is $250\text{ rad/s}$. At resonance, the voltage across the inductance is

A series resonant circuit consists of inductor ' $L$ ' of negligible resistance and a capacitor ' $C$ ' which produces resonant frequency ' $f$ '. If $L$ is changed to 3 L and ' C ' is changed to 6 C, the resonant frequency will become.

LC series resonant circuit produces resonant frequency ' $f$ '. If ' $L$ ' is tripled and ' $C$ ' is increased by $3C$, the resonant frequency will be

In series LCR resonant circuit, the capacitance is changed from C to 3 C. To obtain the same resonant frequency, the inductance should be changed from $L$ to

An inductor of inductance $2\ \mu\text{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}\text{ F}$, where the value of ' $x$ ' is (Take $\pi^2 = 10$)

In series LCR circuit, the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged, the new inductance should be:

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $2.5\text{ nF}$. If resistance of $200\ \Omega$ and $100\text{ mH}$ inductor is being used in the given circuit. The frequency of ac source is _________ $\times 10^{3}\text{ Hz}$ (given $\pi^2 = 10$)

In LCR resonant circuit, the current and voltage have phase difference

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Given below are two statements:

Statement I: In an LCR series circuit, current is maximum at resonance.

Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

In the light of the above statements, choose the correct answer from the options given below:

Which one of the following graphs correctly represents the variation of impedance $(Z)$ of a series LCR circuit with the frequency $(v)$ of applied a.c.?

With gradual increase in frequency of an a.c. supply, the impedance of an LCR series circuit

In LCR series circuit if the frequency is increased, the impedance of the circuit

An inductance of 2 mH, a condenser of $20\ \mu\text{F}$ and a resistance of $50\ \Omega$ are connected in series to an a.c. source. The reactance of inductor and condenser are same. The reactance of either of them will be

A resistor of $50\ \Omega$, inductor of self inductance $\left(\frac{3}{\pi^2}\right)\text{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz. When the voltage and current are in phase, the value of capacitance is (nearly)

In series LCR circuit, 'R' represents resistance of electric bulb. If the frequency of a.c. supply is doubled, the value of inductance ' $L$ ' and capacitance 'C' should be

A series $L - C - R$ circuit containing a resistance ' $R$ ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $V_R$ ' and ' $V_L$ ' respectively, then value of capacitance will be

For the given figure, choose the correct option.

A series LCR circuit containing a resistance ' R ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $V_R$ ' and ' $V_L$ ' respectively, then value of inductance ' $L$ ' will be

$L = 2\text{ H}, C = 5\text{ mF}$ and $R = 12\ \Omega$ are connected in series to an a.c. generator of frequency 50 Hz. Then

In a series LCR circuit, the inductance $L$ is $10\text{ mH}$, capacitance $C$ is $1\ \mu\text{F}$ and resistance $R$ is $100\ \Omega$. The frequency at which resonance occurs is :-

An inductor of inductance 2 $\mu\text{H}$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit $\frac{1}{x}\text{ F}$, where the value of $x$ is ___________.

(Take $\pi = \frac{22}{7}$)

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $\Omega$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.

(Take $\pi^2 = 10$)

Resistor of $2\ \Omega$, inductor of $100\ \mu\text{H}$ and capacitor of $400\text{ pF}$ are connected in series across a source of $e_{\text{rms}} = 0.1$ Volt. At resonance, voltage drop across inductor is

An inductor of $0.5\text{ mH}$, a capacitor of $20\ \mu\text{F}$ and a resistance of $20\ \Omega$ are connected in series with a $220\text{ V}$ a.c. source. If the current is in phase with the e.m.f. the maximum current in the circuit is $\sqrt{x}\text{ A}$. The value of '$x$' is

Given below are two statements:

Statement I: An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.

Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.

In the light of above statements, choose the correct answer form the options given below:

An inductor of $0.5\text{ mH}$, a capacitor of $20\ \mu\text{F}$ and resistance of $20\ \Omega$ are connected in series with a $220\text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}$ A. The value of $x$ is ___________

With increase in frequency of a.c. supply, the impedance of an L-C-R series circuit

With the gradual increase in frequency of an a. c. source, the impedance of an LCR series circuit

A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually, then the electric bulb is found to

Given below are two statements:

Statement I: When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.

Statement II: In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below.

In the circuit shown the ratio of quality factor and the bandwidth is

A series combination of resistor of resistance $100\ \Omega$, inductor of inductance $1\text{ H}$ and capacitor of capacitance $6.25\ \mu\text{F}$ is connected to an ac source. The quality factor of the circuit will be __________

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.

A series LCR circuit is connected to an ac source of $220\text{ V}, 50\text{ Hz}$. The circuit contain a resistance $R = 100\ \Omega$ and an inductor of inductive reactance $X_L = 79.6\ \Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $\mu\text{F}$.

In a series LCR circuit, $C = 2\ \mu\text{F}, L = 1\text{ mH}$ and $R = 10\ \Omega$. The ratio of the energies stored in the inductor and the capacitor, when the maximum current flows in the circuit, is

For the given figures, choose the correct options:

A series $LCR$ circuit consists of $R = 80\ \Omega, X_L = 100\ \Omega$, and $X_C = 40\ \Omega$. The input voltage is 2500 $\cos(100\pi t)\text{ V}$. The amplitude of current, in the circuit, is _________ A.

To increase the resonant frequency in series LCR circuit,

A series LCR circuit with $R = \frac{250}{11}\ \Omega$ and $X_L = \frac{70}{11}\ \Omega$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be _________ $\mu$F. (Take: $\pi = \frac{22}{7}$)

An inductor of 0.5 mH, a capacitor of 200 $\mu$F and a resistor of 2 $\Omega$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ____________ $\times$ 102 Hz.

Given below are two statements:

Statement I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.

Statement II: In ac circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below.

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

A series LCR circuit with inductance 10 H, capacitance 10 $\mu$F, resistance 50 $\Omega$ is connected to an ac source of voltage, V = 200sin(100t) volt. If the resonant frequency of the LCR circuit is v0 and the frequency of the ac source is v, then

In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 $\mu$F and R = 10 $\Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ___________ A.

A series LCR circuit has $L = 0.01\text{ H}, R = 10\ \Omega$ and $C = 1\ \mu\text{F}$ and it is connected to ac voltage of amplitude $(V_m)\ 50\text{ V}$. At frequency $60\%$ lower than resonant frequency, the amplitude of current will be approximately:

For a series LCR circuit, I vs $\omega$ curve is shown:

(a) To the left of $\omega$r, the circuit is mainly capacitive.

(b) To the left of $\omega$r, the circuit is mainly inductive.

(c) At $\omega$r, impedance of the circuit is equal to the resistance of the circuit.

(d) At $\omega$r, impedance of the circuit is 0. Choose the most appropriate answer from the options given below:

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency (f2) and new quality factor (Q2) will be:

(f1 = original resonant frequency, Q1 = original quality factor)

A telegraph line of length 100 km has a capacity of 0.01 $\mu$F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____________ mH. (if $\pi = \sqrt{10}$)

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $212\text{ rad s}^{-1}$ and $232\text{ rad s}^{-1}$. The value of resistance in the circuit is $R = 5\ \Omega$. The self inductance in the circuit is __________ $\text{mH}$.

In an LCR series circuit, an inductor 30 mH and a resistor 1 $\Omega$ are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 45${}^\circ$ is $\frac{1}{x} \times 10^{-3}$ F. Then the value of x is ____________.

In series LCR circuit, at resonance the peak value of current will be [$E_0$ is peak emf, R is resistance, $\omega L$ is inductive reactance and $\omega C$ is capacitive]

In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are

A series LCR circuit of R = 5$\Omega$, L = 20 mH and C = 0.5 $\mu$F is connected across an AC supply of 250 V, having variable frequency. The power dissipated at resonance condition is ______________ $\times$ 102 W.

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8$\Omega$, L = 24 mH and C = 60 $\mu$F. The value of power dissipated at resonant condition is 'x' kW. The value of x to the nearest integer is ____________.

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value:

A resonance circuit having inductance and resistance 2 $\times$ 10$-$4 H and 6.28$\Omega$ respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is ___________. [$\pi$ = 3.14]

A circuit containing resistance R${}_{1}$, inductance L ${}_{1}$ and capacitance C${}_{1}$ connected in series resonates at the same frequency 'f${}_{0}$' as another circuit containing R${}_{2}$, L${}_{2}$ and C${}_{2}$ in series. If two circuits are connected in series then the new frequency at resonance is

A 100$\Omega$ resistance, a 0.1 $\mu$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $\mu$F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ $\times$ 10$-$8 H.

A series L-C-R circuit containing a resistance of $120\ \Omega$ has angular frequency $4 \times 10^{5}\text{ rad s}^{-1}$. At resonance the voltage across resistance and inductor are $60\text{ V}$ and $40\text{ V}$ respectively, then the value of inductance will be

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts as shown in figure. Potential difference across L, C and R is 40V, 10V and 40V, respectively. The amplitude of current flowing through LCR series circuit is 10$\sqrt{2}$ A. The impedance of the circuit is:

Match List - I with List - II

Choose the correct answer from the options given below

Find the peak current and resonant frequency of the following circuit (as shown in figure).

A series LCR circuit containing 5.0 H inductor, 80$\mu$F capacitor and 40$\Omega$ resistor is connected to 230V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

A series L-C-R circuit is designed to resonate at an angular frequency $\omega$0 = 105 rad/s. The circuit draws 16W power from 120V source at resonance. The value of resistance 'R' in the circuit is _________ $\Omega$.

An alternating emf of $0.2\text{ V}$ is applied across an L-C-R series circuit having $R = 4\ \Omega, C = 80\ \mu\text{F}$ and $L = 200\text{ mH}$. At resonance the voltage drop across the inductor is

An AC circuit has R= 100 $\Omega$, C = 2 $\mu$F and L = 80 mH, connected in series. The quality factor of the circuit is:

For an RLC circuit driven with voltage of amplitude vm and frequency $\omega_0 = \frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by:

Which of the following combinations should be selected for better tuning of an L-C-R circuit used for combination?

When resonance is produced in a series LCR circuit, then which of the following is not correct?

The plot given below is of the average power delivered to an LRC circuit versus frequency. The quality factor of the circuit is:

An LCR circuit as shown in the figure is connected to a voltage source $V_{ac}$ whose frequency can be varied. The frequency, at which the voltage across the resistor is maximum, is:

What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 $\mu$F and $\omega$ = 1000 s${}^{-1}$?

In a series resonant $LCR$ circuit, the voltage across $R$ is $100$ volts and $R = 1\text{ k}\Omega$ with $C = 2\ \mu\text{F}.$ The resonant frequency $\omega$ is $200\text{ rad/s}$. At resonance the voltage across $L$ is

The self inductance of the motor of an electric fan is $10\text{ H}$. In order to impart maximum power at $50\text{ Hz}$, it should be connected to a capacitance of