Question

The transfer function of an RLC series circuit when input voltage is fed to \( R, L \) and output voltage is across \( C \) is:

• A. \( \frac{1}{s^2LC + sRL + 1} \)
• B. \( \frac{1}{s^2RL + sLC + 1} \)
• C. \( \frac{1}{s^2RC + sLC + 1} \)
• D. \( \frac{1}{s^2LC + sRC + 1} \)

Hint:

Use voltage division and express each impedance in Laplace domain: \( Z_L = sL, Z_C = 1/sC \).

Answer 1

The Correct Option is D

In an RLC series circuit, applying voltage divider in Laplace domain: \[ V_C(s) = \frac{1/sC}{sL + R + 1/sC} \cdot V(s) \] \[ \Rightarrow \frac{V_C(s)}{V(s)} = \frac{1}{s^2LC + sRC + 1} \]