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 $\mathrm{t}=0$)

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

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 power factor of the circuit containing an inductor of inductance $1.5 \mathrm{H}$ and a resistor of resistance $1500 \mathrm{\Omega }$ at a frequency of $1000 \mathrm{rad}/\mathrm{s}$? Round it to one digit after the decimal point.

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.

$\mathrm{A}$ 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

A circuit containing a $80 \mathrm{mH}$ inductor, and a $60 \mathrm{\mu F}$ capacitor in series is connected to a $230 \mathrm{V}$, $50 \mathrm{Hz}$ supply. The resistance of the circuit is negligible. Obtain the current amplitude.

An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.

The average power in a $L-C-R$ circuit depends upon

When $100 \mathrm{V}$ DC. is applied across a coil, a current of $1 \mathrm{A}$ flows through it. When $100 \mathrm{V}$ AC. of frequency $50 \mathrm{Hz}$ is applied to the same coil, only $0.5 \mathrm{A}$ current flows through it. Calculate resistance, impedance and self inductance of the coil.

Explain the term: Impedance.

A series $L-C-R$ circuit containing $R=20 \mathrm{\Omega }, L=200 \mathrm{mH}$ and $C=40 \mu \mathrm{F}$ is joined to a $120 \mathrm{V}, 60 \mathrm{Hz}$ AC source. Find (i) Total reactance (ii) impedance (iii) power factor (iv) average power.

Write down the expression for impedance, frequency and power factor for a series L-C-R AC circuit?

If $f_{\mathit{r}}$ is the resonant frequency of AC circuit. Give phase relationship between voltage and current for $\left(\mathrm{i}\right) f<f_r$ $\left(\mathrm{ii}\right) f=f_r$ $\left(\mathrm{iii}\right)\mathit{ }f>f_{\mathit{r}}$