$A$ direct current of $10 \,A$ is superimposed on an alternating current $I = 40 \cos \omega t \; (A)$ flowing through a wire. The effective value of the resulting current will be ....... $A$.

$A$ coil has inductance of $0.4 \text{ H}$ and resistance of $8 \Omega$. It is connected to an $AC$ source with peak emf $4 \text{ V}$ and frequency $\frac{30}{\pi} \text{ Hz}$. The average power dissipated in the circuit is (in $\text{ W}$)

$A$ $ 100 \,W $ bulb is connected to an $ AC $ source of $ 220 \,V, 50 \,Hz $. Then the current flowing through the bulb is

An inductor stores $16 \ J$ of magnetic field energy and dissipates $32 \ W$ of thermal energy due to its resistance when an $A.C.$ current of $2 \ A$ $(rms)$ and frequency $50 \ Hz$ flows through it. The ratio of inductive reactance to its resistance is . . . . . . . $(\pi=3.14)$

In a series $LCR$ circuit,$R = 200 \, \Omega$ and the voltage and frequency of the main supply are $220 \, V$ and $50 \, Hz$ respectively. On taking out the capacitance from the circuit,the current lags behind the voltage by $30^\circ$. On taking out the inductor from the circuit,the current leads the voltage by $30^\circ$. The power dissipated in the $LCR$ circuit is......$W$.

$A$ $100 \, \Omega$ resistance and a capacitor of $100 \, \Omega$ reactance are connected in series across a $220 \, V$ source. When the capacitor is $50\%$ charged,the peak value of the displacement current is.....$A$