In a series $LCR$ circuit,operated with an $ac$ of angular frequency $\omega$,the total impedance is

  • A
    ${[{R^2} + {(L\omega - C\omega )^2}]^{1/2}}$
  • B
    ${\left[ {{R^2} + {{\left( {L\omega - \frac{1}{{C\omega }}} \right)}^2}} \right]^{1/2}}$
  • C
    ${\left[ {{R^2} + {{\left( {L\omega - \frac{1}{{C\omega }}} \right)}^2}} \right]^{ - 1/2}}$
  • D
    ${\left[ {{{(R\omega )}^2} + {{\left( {L\omega - \frac{1}{{C\omega }}} \right)}^2}} \right]^{1/2}}$

Explore More

Similar Questions

An $AC$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased,

$A$ circuit element $X$ when connected to an a.c. supply of peak voltage $100\,V$ gives a peak current of $5\,A$ which is in phase with the voltage. $A$ second element $Y$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If $X$ and $Y$ are connected in series to the same supply,what will be the rms value of the current in ampere?

The diagram shows a capacitor $C$ and a resistor $R$ connected in series to an $ac$ source. $V_1$ and $V_2$ are voltmeters and $A$ is an ammeter. Consider the following statements:
$I$. Readings in $A$ and $V_2$ are always in phase.
$II$. Reading in $V_1$ lags behind the reading in $V_2$ by $\frac{\pi}{2}$.
$III$. Readings in $A$ and $V_1$ are always in phase.
Which of these statements is/are correct?

In a series $LR$ circuit,$X_L=R$,the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C=X_L$ is added to the circuit,the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be

The current $I$,potential difference $V_L$ across the inductor,and potential difference $V_C$ across the capacitor in the circuit as shown in the figure are best represented vectorially as:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo