Question

For a series LCR circuit, $I$ vs $\omega$ curve is shown :
(a) To the left of $\omega_{r}$, the circuit is mainly capacitive.
(b) To the left of $\omega_{r}$, the circuit is mainly inductive.
(c) At $\omega_{r}$, impedance of the circuit is equal to the resistance of the circuit.
(d) At $\omega_{r}$, impedance of the circuit is $0$ .

Choose the most appropriate answer from the options given below :

• A. (a) and (d) only
• B. (b) and (d) only
• C. (a) and (c) only
• D. (b) and (c) only

Answer 1

Answer: (C)

at $ \omega_{ r }, X _{ C }= X _{ L } $
$\Rightarrow \frac{1}{\omega_{ r } C }=\omega_{ r } L$
So if $\omega < \omega_{ r }$ then $x _{ C }$ will increase and $X _{ L }$ will decrease.
Hence to left of $\omega_{ r }$ circuit is capacitive
$Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}$
at $\omega_{r}, Z=\sqrt{R^{2}+O^{2}}=R(C)$