In an $RC$ $AC$ circuit,the maximum voltage and maximum current are $100 \ V$ and $1.1 \ A$ respectively. If $X_{C} = 60 \ \Omega$ and $R = 80 \ \Omega$,then the power consumed in the circuit will be . . . . . . . (in $W$)

$A$ bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased,while keeping the voltage of the source constant,then

$A$ $220\, V$,$50\, Hz$ $ac$ source is connected to an inductance of $0.2\, H$ and a resistance of $20\, \Omega$ in series. What is the current in the circuit (in $, A$)?

$A$ lamp is connected in series with a capacitor and an $AC$ source. What happens if the capacitance of the capacitor is reduced?

In an $LR$ circuit,the value of $L$ is $(\frac{0.3}{\pi}) \ H$ and the value of $R$ is $40 \ \Omega$. If an alternating e.m.f. of $230 \ V$ at $50 \ Hz$ is connected to the circuit,what are the impedance and the current in the circuit,respectively?

When an $AC$ source of $e.m.f.$ $e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f.$ $e$ and the current $i$ in the circuit is observed to be $\pi/4$,as shown in the diagram. If the circuit consists possibly only of $RC$ or $LC$ in series,find the relationship between the two elements.