In a series $LCR$ circuit,$R=300 \Omega$,$L=0.9 \text{ H}$,$C=2 \mu\text{F}$,and $\omega=1000 \text{ rad/s}$. The impedance of the circuit is: (in $Omega$)

When an $AC$ source of emf $E$ with angular frequency $\omega = 100 \text{ rad/s}$ is connected across a circuit,the phase difference between $E$ and current $I$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consists of only $RC$ or $RL$ in series,then:

$A$ pure inductor of $25.48 \ mH$ and a pure resistor of $8 \ \Omega$ are connected in series with an $AC$ source of frequency $50 \ Hz$. The phase difference between current $(I)$ and voltage $(V)$ in this circuit is . . . . . . . (in $^{\circ}$)

$A$ 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?

An $A.C.$ source is connected to a series $LCR$ circuit. If the voltage across $R$ is $40 \,V$, the voltage across $L$ is $80 \,V$, and the voltage across $C$ is $40 \,V$, then the e.m.f. '$e$' of the $A.C.$ source is:

An a.c. source of frequency $f$ is connected to a circuit containing an inductance $L$ and resistance $R$ in series. The impedance of this circuit is