AC Voltage Applied to a Series LCR Circuit

What is damped and undamped oscillation?

In $\mathrm{RLC}$ circuits, the circuit oscillates if _____ is zero.

In damped oscillation of LCR series circuit charge amplitude is expressed as ( where ${\mathrm{q}}_{\mathrm{m}}=$charge amplitude at $\mathrm{t}=0$)

For small value of resistance damped oscillation of LCR circuit becomes as undamped LC oscillation in respect of angular frequency.

According to voltage vs $\mathrm{\omega t}$ graph in LCR series circuit, how phasor diagram will be represented.

In LCR series circuit amplitude of voltage across inductor is ( if Peak value of current$={\mathrm{I}}_0$ and inductive reactance$={\mathrm{X}}_{\mathrm{L}}=\mathrm{\omega L}$)

When resistance $R$ is connected in series with an element $A$, the electric current is found to be lagging behind the voltage $V$ by angle $30°$. When the same resistance is connected in series with element $B$, current leads by $60°$. When $R\text{,} A\text{, }B$ are connected in series, the current now leads voltage by $\theta$ which is equal to ${\tan }^{-1}\left(K/\sqrt{3}\right),$ then the value of $K$ is (assume same $AC$ source is used in all cases)

In the series $L-C-R$ circuit, the voltmeter and ammeter readings are respectively $a \mathrm{V}$ and $b \mathrm{A}$. Find the value of $\frac{a}{100}+b$.

In AC series circuit, the resistance, inductive reactants and capacitive reactants are $3\mathrm{ohm}, 10\mathrm{ohm} \mathrm{and} 14\mathrm{ohm}$ respectivity. Find the impedance of the circuit.

When $100 \mathrm{V} \mathrm{DC}$ is applied across a solenoid, a steady current of $1 \mathrm{A}$ flows in it. When $100 \mathrm{V} \mathrm{AC}$ is applied across the same solenoid, the current drops to $0.5 \mathrm{A}.$If the frequency of the $\mathrm{AC}$ source is $150\sqrt{3}/\pi \mathrm{Hz}$ the impedance and inductance of the solenoid are :

Assertion : In a series $R, L, C$ circuit if $V_R, V_1,$ and $V_c$ denote $r m s$ voltage across $R, L$ and $C$ respectively and $V_s$ is the rms voltage across the source, then $V_s=V_R+V_L+V_c.$

Reason:  Kirchoff voltage law is valid only for $DC$ circuit, but it is not valid for $AC$ circuit.

What is the impedance of a series RLC circuit with resistance $R=1354 \mathrm{\Omega }$, capacitance $C=2 \mathrm{\mu F}$ and inductance $L=2 \mathrm{H}$ when the frequency of the source is $150 \mathrm{Hz}$. Round the answer to the nearest integer.

In the figure shown the reading of voltmeters are $V_1=40 \mathrm{V}, V_2$ $=40 \mathrm{V}$ and $V_3=10 \mathrm{V}.$ Find the peak value of $emf$

An AC source of angular frequency $\mathrm{\omega }$ is fed across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If now the frequency of source is changed to $\frac{\mathrm{\omega }}{3}$ (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency $\mathrm{\omega }$ will be,

$\mathrm{A}$ steady current of $2 \mathrm{A}$ flows when an inductor of inductance $2\mathrm{mH}$ is connected to ac source of emf $10 \mathrm{V}$. Now $\mathrm{a}$ capacitor of capacity $2\mathrm{\mu F}$ is connected in series. If the current in the circuit is along the emf, the rms value of the current is

For the ac circuit shown below, phase difference between $\mathrm{emf}$ and current is $\frac{\pi }{4}$ radian as shown in the graph. If the impedance of the circuit is $1414 \mathrm{\Omega }$ then the values of $P$ and $Q$ are;

In an $\mathrm{LCR}$ circuit, inductive reactance and capacitive reactance was found to be equal. The resistance was found to be $20 \mathrm{\Omega }.$ The probable impedance of the combination is

In the given circuit, the reading of voltmeter $V_{\mathrm{L}}$ and $V_{\mathrm{C}}$ are $300 \mathrm{V}$ each. The reading of the voltmeter $V_{\mathrm{R}}$ and ammeter $\mathrm{A}$ are respectively,