Question

A series LRC circuit is activated by a sinusoidal ac volage e = E${}_o$ sin $\omega$t, with varying frequency $\omega$. In Column I, different frequency values are given and in Column II, different responses of the circuit are shown. One or more of items in Column II may match with any of the frequencies given in Column I. $[{\omega }_o=\frac{1}{\sqrt{LC}}]$

Answer 1

$e=E_{o}Sinwt$ $Z=\sqrt{R^2+(X_L-X_C{)}^2}$
$W_o=\frac{1}{\sqrt{LC}}\Rightarrow X_L=X_C$
A) if $w>w_o,$ the circuit will be inductive
$\therefore$ voltage will lead current
B) $W=\sqrt{\frac{1}{LC}+\frac{R}{4L^2}}-\frac{R}{2L}>w_o$
$\therefore w>w_o\Rightarrow$ voltage leads current because circuit is inductive.
C) $w<w_o\Rightarrow$ circuit is capacitive
$\therefore$ current leads the voltage
D) $w=w_o\Rightarrow$ P are resistive impedance also, $cos\varphi =1$
$\therefore Power=Pmax$