In the circuit shown below, \( R_1 = 2 \, \Omega \), \( R_2 = 1 \, \Omega \), \( L_1 = 2 \, H \), and \( L_2 = 0.5 \, H \). Which of the following describe(s) the characteristics of the circuit?
In the circuit shown below, \( R_1 = 2 \, \Omega \), \( R_2 = 1 \, \Omega \), \( L_1 = 2 \, H \), and \( L_2 = 0.5 \, H \). Which of the following describe(s) the characteristics of the circuit?
Show Hint
- Second order high pass filter
- Second order low pass filter
- Underdamped system
- Overdamped system
The Correct Option is B, D
Solution and Explanation
Step 1: Identify the nature of the circuit.
The circuit contains inductors and resistors, and based on its configuration, we can expect the behavior of the system to be defined by the resonance and damping factors. For a second-order system like this, the quality factor (\( Q \)) and the damping factor (\( \zeta \)) will determine whether the system is underdamped or overdamped.
- A second-order low pass filter will allow low-frequency signals to pass through while attenuating higher-frequency signals. Given the resistor-inductor arrangement, this circuit is likely a low-pass filter.
- To determine whether the system is overdamped or underdamped, we calculate the damping factor. The general form of the damping factor \( \zeta \) for an RLC circuit is:
\[
\zeta = \frac{R}{2} \sqrt{\frac{C}{L}}
\]
where \( R \) is the total resistance, \( C \) is the total capacitance, and \( L \) is the inductance. In this case, the circuit is likely overdamped due to the relatively high resistance compared to the inductance values. This suggests that the circuit will not exhibit oscillatory behavior (underdamped) and instead will have a smooth response to input signals.
Step 2: Verify the options.
- (A) Second order high pass filter: The circuit is not a high-pass filter since it primarily allows low-frequency signals to pass and attenuates high-frequency signals.
- (B) Second order low pass filter: This is correct because the circuit's characteristics match those of a second-order low pass filter.
- (C) Underdamped system: This is incorrect because the damping factor is high enough to make the system overdamped.
- (D) Overdamped system: This is correct because the resistance is relatively high compared to the inductance, resulting in an overdamped response.
Thus, the correct answer is (B) Second order low pass filter and (D) Overdamped system.
Final Answer: (B) Second order low pass filter, (D) Overdamped system
Questions Asked in GATE BM exam
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
- Had I learnt acting as a child, I ________ a famous film star.
Select the most appropriate option to complete the above sentence. - The duration of action potential in a ventricular muscle cell of a human heart ranges from ________ milliseconds.
- GATE BM - 2025
- General Physiology