For the network shown in the figure if the switch is closed at t = 0, and when \(\frac{R}{2 L}<\frac{1}{\sqrt{L C}}\), which one of the following statements is correct?

Question

Question

This question was previously asked in

UPSC ESE (Prelims) Electronics and Telecommunication Engineering 19 Feb 2023 Official Paper

Answer 1

Concept:

In a series RLC circuit, the conditions for different nature of damping are:

Over damped: \({\left( {\frac{R}{{2L}}} \right)^2} > \frac{1}{{LC}}\)

Under damped: \({\left( {\frac{R}{{2L}}} \right)^2} < \frac{1}{{LC}}\)

Critically damped: \({\left( {\frac{R}{{2L}}} \right)^2} = \frac{1}{{LC}}\)

Important Points

Underdamped: This condition occurs when the resistance is not sufficient to prevent the oscillations, but enough to cause them to decay over time.The system oscillates with a frequency lower than the natural frequency of the circuit due to the damping effect.
Critically Damped: This is the threshold condition between oscillatory and non-oscillatory behavior. The system returns to equilibrium as quickly as possible without oscillating. This is often desired in systems where quick settling is crucial, such as in control systems.
Overdamped: In this case, the resistance is so high that it suppresses oscillations completely. The system slowly returns to equilibrium without oscillating. This condition is less efficient in terms of speed as it takes longer to reach equilibrium compared to a critically damped system.