$A$ series $LR$ circuit is connected to a voltage source with $V(t) = V_0 \sin \omega t$. After a very large time,how does the current $I(t)$ behave? (Given: $t_0 \gg \frac{L}{R}$)

The output of a step-down transformer is measured to be $48 \,V$ when connected to a $12 \,W$ bulb. The value of peak current is

The following figure shows an $AC$ generator connected to a 'black box' through a pair of terminals. The box contains possible $R, L, C$ or their combination,whose elements and arrangements are not known to us. Measurements outside the box reveal that $e = 75 \sin(\omega t) \text{ V}$ and $i = 1.5 \sin(\omega t + 45^\circ) \text{ A}$. Then,the wrong statement is:

Is the current distribution shown in the figure possible?

An electrical device draws $2 \, kW$ power from $AC$ mains $(V_{rms} = 223 \, V = \sqrt{50000} \, V)$. The current lags in phase by $\tan \phi = -\frac{3}{4}$ compared to the voltage. Find $(i)$ $R$,$(ii)$ $X_C - X_L$,and $(iii)$ $I_M$. Another device has twice the values for $R$,$X_C$,and $X_L$. How are the answers affected?

Match the List-$I$ with List-$II$.

List-$I$	List-$II$
$A$. $AC$ generator	$I$. Presence of both $L$ and $C$
$B$. Transformer	$II$. Electromagnetic Induction
$C$. Resonance phenomenon to occur	$III$. Quality factor
$D$. Sharpness of resonance	$IV$. Mutual Inductance

Choose the correct answer from the options given below: