The input to a series $\text{RLC}$ circuit is a sinusoidal voltage source and the output is the current in the circuit. Which of the following is true about the magnitude frequency response of this system?
- Dependending on the values of $\text{R, L}$ and $\text{C}$, a steady state may not exist, and the magnitude frequency response is not well-defined.
- It is low-pass with $3 \mathrm{~dB}$ bandwidth $1 /(2 \pi \sqrt{\text{LC}})$.
- It is high-pass with $3 \mathrm{~dB}$ bandwidth $1 /(2 \pi \sqrt{\text{LC}})$.
- It is low-pass and the $3\text{-dB}$ bandwidth depends on all: $\text{R, L, C}$.
- It is $0$ at $\text{DC},$ decays to zero as frequency increases to infinity, and has a maximum at $1 /(2 \pi \sqrt{\text{LC}})$.