$A$ 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 $\text{ A}$)

$A$ sinusoidal voltage with a frequency of $50 \ Hz$ is applied to a series $LCR$ circuit with a resistance of $5 \ \Omega$,inductance of $20 \ mH$ and a capacitance of $500 \ \mu F$. The magnitude of impedance of the circuit is close to (in $\Omega$)

Two coils require $20 \ min$ and $60 \ min$ respectively to produce the same amount of heat energy when connected separately to the same source. If they are connected in parallel to the same source,the time required to produce the same amount of heat by the combination of coils will be . . . . . . $min$.

In a radio receiver,the short wave and medium wave stations are tuned by using the same capacitor but coils of different inductance $L_s$ and $L_m$ respectively. Then:

$A$ capacitance of $\left(\frac{10^{-3}}{2 \pi}\right) F$,an inductance of $\left(\frac{100}{\pi}\right) mH$,and a resistance of $10 \Omega$ are connected in series with an $AC$ voltage source of $220 V, 50 Hz$. The phase angle of the circuit is (in $^{\circ}$)

The figure shows the variation of $R$,$X_L$,and $X_C$ with frequency $f$ in a series $L-C-R$ circuit. For what frequency point is the circuit capacitive?