An LCR series circuit is connected to an exte | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) In an $LCR$ series circuit,the amplitude of the current is given by $I_0 = \frac{E_0}{Z}$,where $Z = \sqrt{R^2 + (X_L - X_C)^2}$.For the current a

Vedclass · Accepted Answer

$\frac{100}{\pi^2}$

Vedclass · Answer

(A) In an $LCR$ series circuit,the amplitude of the current is given by $I_0 = \frac{E_0}{Z}$,where $Z = \sqrt{R^2 + (X_L - X_C)^2}$.For the current amplitude to be maximum,the impedance $Z$ must be minimum.This occurs at resonance,where $X_L = X_C$.Given the $emf$ equation $e = 200 \sin(100 \pi t) \ V$,the angular frequency is $\omega = 100 \pi \ rad/s$.The condition for resonance is $\omega L = \frac{1}{\omega C}$.Substituting the given values: $100 \pi 	imes L = \frac{1}{100 \pi 	imes 1 	imes 10^{-6}}$.$L = \frac{1}{(100 \pi)^2 	imes 10^{-6}} = \frac{1}{10000 \pi^2 	imes 10^{-6}} = \frac{1}{10^{-2} \pi^2} = \frac{100}{\pi^2} \ H$.

An $LCR$ series circuit is connected to an external $emf$,$e = 200 \sin(100 \pi t) \ V$. The values of capacitance and resistance in the circuit are $1 \ \mu F$ and $100 \ \Omega$ respectively. The amplitude of current in the circuit is maximum when the inductance is (in henry):

Similar Questions

In a series $R-L-C$ $AC$ circuit,for a particular value of $R, L$ and $C$,the power supplied by the source is $P$ at resonance. If the value of inductance is halved,then the power from the source again at resonance is $P'$. Then:

An $LC$ circuit consists of a capacitor and a coil with a large number of turns. Suppose all the linear dimensions of all elements of the circuit are increased by a factor of $2$ while keeping the number of turns on the coil constant. How much does the resonant frequency of the circuit change?

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

In an $LCR$ series resonance circuit, choose the wrong statement.

An alternating e.m.f. of $0.2 \, V$ is applied across an $LCR$ series circuit having $R=4 \, \Omega$, $C=80 \, \mu F$, and $L=200 \, mH$. At resonance, the voltage drop across the inductor is (in $V$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module