Resonance in a Series LCR Circuit

Graph showing variation of current with frequency of $AC$ source in a series $LCR$ circuit is,

In the following circuit the readings of AC voltmeters and ammeters will be respectively-

The inductance of the oscillatory circuit of the radio station is $10 \mathrm{mH}$ and its capacitance is $0.25 \mathrm{\mu F}$. Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light $=3.0\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1},\mathrm{ }\mathrm{\pi }=3.14$)

The inductance of the oscillatory circuit of the radio station is $10 \mathrm{mH}$ and its capacitance is $0.25 \mathrm{\mu F}$. Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light $=3.0\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1},\mathrm{ }\mathrm{\pi }=3.14$)

A source of $V=15\cos \omega t \mathrm{V}$ is connected to a series $L-C-R$ circuit having $L=10 \mathrm{mH}$, $R=3 \Omega$ and $C=1 \mathrm{\mu F}$. Find the peak value of current at frequency $10 \%$ less than the resonant frequency.

Which one is the expression of resonant frequency in a series resonant circuit?

In LCR alternating circuit, $R=10 \mathrm{\Omega }$, $X_L=100 \mathrm{\Omega }$ and $X_C=100 \mathrm{\Omega }$. What is the impedance of the circuit in Ohms?

A parallel L-C circuit comprises of a 5H inductor and $5\mathrm{\mu F}$ capacitor. The resonant frequency of the circuit in $\mathrm{Hz}$ is 

In the given figure, which point shows the resonant state?

A circuit draws a power of $550$ $\mathrm{W}$ from a source of $220$ $\mathrm{V}$, $50$ $\mathrm{Hz}$. The power factor of the circuit is $0.8$ and the current lags in phase behind the potential difference. To make the power factor of the circuit as unity, the capacitance connected with the circuit in series is$15\times n \mathrm{\mu F}$. Find the value of $n$.

The given figure represents the phasor diagram of a series $\mathrm{LCR}$ circuit connected to an ac source. At the instant $t\text{'}$t' when the source voltage is given by $V=V_0\cos \left(\omega t^{\text{'}}\right)$, the current in the circuit will be :

In the $RLC$ circuit in the figure, $R=60 \Omega ,$ $L=3 \mathrm{mH}, C=4 \mathrm{mF},$ and the source of time varying emf has a peak voltage of $120 \mathrm{V}.$ What should the angular frequency of the source, $\omega$, be to produce the largest current in the resistor?

If value of $R$ is changed, then :-

The resonance frequency of the tank circuit of an oscillator when $L=\frac{10}{{\pi }^2} \mathrm{mH}$ and $C=0.04 \text{μF}$ are connected in parallel is

In a series resonant circuit, the AC voltage across resistance $R$, inductor $L$ and capacitor $C$ are $5 \mathrm{V}, 10 \mathrm{V} \mathrm{and} 10 \mathrm{V}$, respectively. The AC voltage applied to the current will be

In $LCR$ series circuit, the resonance condition in terms of capacitive reactance $\left(X_C\right)$ and inductive reactance $\left(X_L\right)$ is

The inductance of the oscillatory circuit of the radio station is $10 \mathrm{mH}$ and its capacitance is $0.25 \mathrm{\mu F}$. Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light $=3.0\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1},\mathrm{ }\mathrm{\pi }=3.14$)

A $1\mathrm{0 }\mathrm{\Omega }$ resistance, $5 \mathrm{mH}$ coil and $1\mathrm{0 }\mathrm{\mu F}$ capacitor are joined in series. When a variable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is halved, the resonance frequency:

A series $L-C-R$ circuit of $L=200 \mathrm{mH}$, $C=500 \mathrm{\mu F}$, $R=100 \mathrm{\Omega }$ is connected to $100 \mathrm{V}$ AC source.

Find-

(i) Frequency at which power factor of circuit is $1$.

(ii) Peak value of current at this frequency.

(iii) Quality factor 

Find the resonance frequency of series $L-C-R$ series circuit containing $L=0.1 \mathrm{H},$$C=20 \mathrm{\mu F}$, $R=10 \mathrm{\Omega }$