In a series $LCR$ circuit, the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$, then the peak voltage across the inductor is

$A$ 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?

$A$ radio can tune over the frequency range of a portion of $MW$ broadcast band: ($800 \;kHz$ to $1200 \;kHz$). If its $LC$ circuit has an effective inductance of $200 \;\mu H$,what must be the range of its variable capacitor?

$A$ sinusoidal voltage of peak value $283 \, V$ and angular frequency $320 \, rad/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega$,$L = 25 \, mH$,and $C = 1000 \, \mu F$. The total impedance and the phase difference between the voltage across the source and the current will respectively be:

If $E = 200\,V$,$R = 25\,\Omega$,$L = 2\,H$,and $C = 2\,\mu F$ and the frequency is variable,then the current at $f = 0$ and $f = \infty$ will be respectively:

An inductor and a resistor in series are connected to an $A.C.$ supply of variable frequency. As the frequency of the source is increased,the phase angle between current and the potential difference across $L$ will