$A$ resistor of resistance $30 \Omega$, an inductor of reactance $10 \Omega$, and a capacitor of reactance $10 \Omega$ are connected in series to an $AC$ voltage source $V = 300 \sqrt{2} \sin(\omega t)$. The current in the circuit is . . . . . . (in $\text{ A}$)

In an $LCR$ circuit,the potential difference between the terminals of the inductor is $60\,V$,between the terminals of the capacitor is $30\,V$,and between the terminals of the resistor is $40\,V$. The supply voltage will be equal to ......$V$.

In the given circuit,the magnitudes of $V_{L}$ and $V_{C}$ are twice that of $V_{R}$. Given that $f=50\,Hz$ and $R=5\,\Omega$,the inductance of the coil is $\frac{1}{K\pi}\,mH$. The value of $K$ is:

In a series $LCR$ circuit, $R = 10 \ \Omega$ and the impedance $Z = 30 \ \Omega$. An $r.m.s.$ voltage of $210 \text{ V}$ is applied across the circuit. The true power consumed in the $AC$ circuit is: (in $\text{ W}$)

An inductor $20 \, mH$,a capacitor $50 \, \mu F$ and a resistor $40 \, \Omega$ are connected in series across a source of emf $V = 10 \, \sin \, 340t$. The power loss in the $A.C.$ circuit is ...... $W$.

An inductor of $10 \text{ mH}$, capacitor of $0.1 \text{ } \mu\text{F}$ and a resistor of $100 \text{ } \Omega$ are connected in series across an $a.c.$ power supply of $220 \text{ V}$, $70 \text{ Hz}$. The power factor of the given circuit is $0.5$. The difference between the inductive reactance and capacitive reactance is $\sqrt{3}\alpha \text{ } \Omega$. The value of $\alpha$ is . . . . . . .