Question

An RLC series circuit has \[ R=1\Omega,\quad L=1H,\quad C=1F. \] Damping ratio of the circuit will be

• A. Greater than unity
• B. Unity
• C. \(0.5\)
• D. Zero

Hint:

For a series RLC circuit, \[ \zeta=\frac{R}{2}\sqrt{\frac{C}{L}}. \] Remember: \[ \zeta<1 \Rightarrow \text{Underdamped} \] \[ \zeta=1 \Rightarrow \text{Critically damped} \] \[ \zeta>1 \Rightarrow \text{Overdamped} \]

Answer 1

The Correct Option is C

Concept: The damping ratio of a series RLC circuit is given by \[ \zeta = \frac{R}{2} \sqrt{\frac{C}{L}}. \] It indicates whether the circuit is underdamped, critically damped, or overdamped.

Step 1: Write the damping ratio formula.
\[ \zeta = \frac{R}{2} \sqrt{\frac{C}{L}}. \]

Step 2: Substitute the given values.
Given, \[ R=1\Omega, \qquad L=1H, \qquad C=1F. \] Therefore, \[ \zeta = \frac{1}{2} \sqrt{\frac{1}{1}}. \] \[ = \frac12. \]

Step 3: Interpret the result.
Since \[ \zeta=0.5<1, \] the circuit is underdamped. Hence the damping ratio is \[ \boxed{0.5}. \]