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Frequency Domain Analysis (Polar & Bode Plot) MCQs for Electrical Engineering (EE) Exam
It covers all Important Questions with answers on Frequency Domain Analysis (Polar & Bode Plot) for the Electrical Engineering (EE) exam. The questions are based on important topics. Details about the questions:- Topic: Frequency Domain Analysis (Polar & Bode Plot)
- Type of Questions: MCQs with solutions
- Number of Questions: 50
- You can attempt them on EduRev to score high in Electrical Engineering (EE) exam.
If the constant 'k' is negative, then what would be its contribution to the phase plot:- a)90 degrees
- b)45 degrees
- c)180 degrees
- d)0 degree
Correct answer is option 'C'. Can you explain this answer?
If the constant 'k' is negative, then what would be its contribution to the phase plot:
a)
90 degrees
b)
45 degrees
c)
180 degrees
d)
0 degree
 | Kunal Yadav answered |
Explanation:
When analyzing the phase plot of a system, we consider the effect of each component separately and then combine them to determine the overall phase shift. In this case, we are considering the effect of a negative constant, denoted as k, on the phase plot.
Effect of a Negative Constant on the Phase Plot:
When the constant k is negative, it means that it has a negative value. This negative value contributes a phase shift to the overall phase plot.
Contribution of a Negative Constant to the Phase Plot:
The contribution of a negative constant to the phase plot can be determined by considering the properties of the complex plane and the concept of complex numbers.
In the complex plane, the negative real axis is oriented at an angle of 180 degrees with respect to the positive real axis. This means that any negative value on the real axis will have a phase shift of 180 degrees.
Since the constant k is negative, its contribution to the phase plot is a phase shift of 180 degrees.
Therefore, the correct answer is option 'C' - 180 degrees.
Summary:
- When the constant k is negative, it contributes a phase shift to the phase plot.
- The contribution of a negative constant to the phase plot is a phase shift of 180 degrees.
- Therefore, the correct answer is option 'C' - 180 degrees.
When analyzing the phase plot of a system, we consider the effect of each component separately and then combine them to determine the overall phase shift. In this case, we are considering the effect of a negative constant, denoted as k, on the phase plot.
Effect of a Negative Constant on the Phase Plot:
When the constant k is negative, it means that it has a negative value. This negative value contributes a phase shift to the overall phase plot.
Contribution of a Negative Constant to the Phase Plot:
The contribution of a negative constant to the phase plot can be determined by considering the properties of the complex plane and the concept of complex numbers.
In the complex plane, the negative real axis is oriented at an angle of 180 degrees with respect to the positive real axis. This means that any negative value on the real axis will have a phase shift of 180 degrees.
Since the constant k is negative, its contribution to the phase plot is a phase shift of 180 degrees.
Therefore, the correct answer is option 'C' - 180 degrees.
Summary:
- When the constant k is negative, it contributes a phase shift to the phase plot.
- The contribution of a negative constant to the phase plot is a phase shift of 180 degrees.
- Therefore, the correct answer is option 'C' - 180 degrees.
Consider a feedback system with gain margin of about 30. At what point does Nyquist plot crosses negative real axis?- a)-3
- b)-0.3
- c)-30
- d)-0.03
Correct answer is option 'B'. Can you explain this answer?
Consider a feedback system with gain margin of about 30. At what point does Nyquist plot crosses negative real axis?
a)
-3
b)
-0.3
c)
-30
d)
-0.03
 | Sharmila Kulkarni answered |
Nyquist Plot and Gain Margin
Nyquist plot is a graphical representation of a system's frequency response. It is used to analyze the stability of a feedback system. The Nyquist plot is a plot of the frequency response of a system in the complex plane. The gain margin of a feedback system is the amount of gain that the system can handle before it becomes unstable. It is defined as the amount of gain that causes the Nyquist plot to cross the negative real axis.
Answer Explanation
Given that the gain margin of the feedback system is about 30, we can determine at what point the Nyquist plot crosses the negative real axis by using the Nyquist stability criterion. The Nyquist stability criterion states that the number of encirclements of the -1 point in the Nyquist plot is equal to the number of unstable poles of the closed-loop transfer function.
Since the gain margin is about 30, the Nyquist plot will cross the negative real axis at a point where the magnitude of the complex number is equal to 1/30. This is because the gain margin is the reciprocal of the point where the Nyquist plot crosses the negative real axis. Therefore, the Nyquist plot will cross the negative real axis at a frequency of -0.3, which corresponds to a magnitude of 1/30.
Thus, the correct answer is option B, -0.3.
Nyquist plot is a graphical representation of a system's frequency response. It is used to analyze the stability of a feedback system. The Nyquist plot is a plot of the frequency response of a system in the complex plane. The gain margin of a feedback system is the amount of gain that the system can handle before it becomes unstable. It is defined as the amount of gain that causes the Nyquist plot to cross the negative real axis.
Answer Explanation
Given that the gain margin of the feedback system is about 30, we can determine at what point the Nyquist plot crosses the negative real axis by using the Nyquist stability criterion. The Nyquist stability criterion states that the number of encirclements of the -1 point in the Nyquist plot is equal to the number of unstable poles of the closed-loop transfer function.
Since the gain margin is about 30, the Nyquist plot will cross the negative real axis at a point where the magnitude of the complex number is equal to 1/30. This is because the gain margin is the reciprocal of the point where the Nyquist plot crosses the negative real axis. Therefore, the Nyquist plot will cross the negative real axis at a frequency of -0.3, which corresponds to a magnitude of 1/30.
Thus, the correct answer is option B, -0.3.
The inverse polar plot of the open loop transfer function, 
will be re presented by- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The inverse polar plot of the open loop transfer function, will be re presented by
will be re presented bya)
b)
c)
d)
 | Lavanya Menon answered |
Given, G(s) = (1+sT)/(sT)
The inverse polar plot of G(jω) is the polar plot of 1/G(jω)
Thus,
and
Hence, inverse polar plot will be as show below,
The inverse polar plot of G(jω) is the polar plot of 1/G(jω)
Thus,
and
Hence, inverse polar plot will be as show below,
If a system has an open loop transfer function 1-s / 1+s, then the gain of the system at frequency of 1 rad/s will be- a)1
- b)1/2
- c)Zero
- d)-1
Correct answer is option 'D'. Can you explain this answer?
If a system has an open loop transfer function 1-s / 1+s, then the gain of the system at frequency of 1 rad/s will be
a)
1
b)
1/2
c)
Zero
d)
-1
 | Anuj Rane answered |
Open Loop Transfer Function
The open loop transfer function of a system represents the relationship between the input and output of a system without any feedback. It is denoted by G(s) and is expressed as the ratio of the Laplace transform of the output to the Laplace transform of the input.
G(s) = Y(s) / X(s)
Where:
G(s) - open loop transfer function
Y(s) - Laplace transform of the output
X(s) - Laplace transform of the input
Given Transfer Function
In this question, the given open loop transfer function is 1 - s / 1 + s.
Frequency Response of a System
To determine the gain of a system at a specific frequency, we substitute jω for s in the transfer function, where ω represents the angular frequency in radians per second.
G(jω) = Y(jω) / X(jω)
To find the gain at a specific frequency, we substitute ω = 1 rad/s in the transfer function and evaluate the expression.
Gain at Frequency ω = 1 rad/s
Substituting ω = 1 rad/s in the transfer function:
G(j1) = Y(j1) / X(j1)
Calculating the Gain
G(j1) = (1 - j) / (1 + j)
To calculate the gain, we need to find the modulus of this complex number.
|G(j1)| = sqrt((1 - j)^2) / sqrt((1 + j)^2)
Simplifying the expression:
|G(j1)| = sqrt(1^2 + (-1)^2) / sqrt(1^2 + 1^2)
|G(j1)| = sqrt(1 + 1) / sqrt(1 + 1)
|G(j1)| = sqrt(2) / sqrt(2)
|G(j1)| = 1
Hence, the gain of the system at a frequency of 1 rad/s is 1.
Conclusion
The correct answer is option 'A' - 1. The gain of the system at a frequency of 1 rad/s is 1.
The open loop transfer function of a system represents the relationship between the input and output of a system without any feedback. It is denoted by G(s) and is expressed as the ratio of the Laplace transform of the output to the Laplace transform of the input.
G(s) = Y(s) / X(s)
Where:
G(s) - open loop transfer function
Y(s) - Laplace transform of the output
X(s) - Laplace transform of the input
Given Transfer Function
In this question, the given open loop transfer function is 1 - s / 1 + s.
Frequency Response of a System
To determine the gain of a system at a specific frequency, we substitute jω for s in the transfer function, where ω represents the angular frequency in radians per second.
G(jω) = Y(jω) / X(jω)
To find the gain at a specific frequency, we substitute ω = 1 rad/s in the transfer function and evaluate the expression.
Gain at Frequency ω = 1 rad/s
Substituting ω = 1 rad/s in the transfer function:
G(j1) = Y(j1) / X(j1)
Calculating the Gain
G(j1) = (1 - j) / (1 + j)
To calculate the gain, we need to find the modulus of this complex number.
|G(j1)| = sqrt((1 - j)^2) / sqrt((1 + j)^2)
Simplifying the expression:
|G(j1)| = sqrt(1^2 + (-1)^2) / sqrt(1^2 + 1^2)
|G(j1)| = sqrt(1 + 1) / sqrt(1 + 1)
|G(j1)| = sqrt(2) / sqrt(2)
|G(j1)| = 1
Hence, the gain of the system at a frequency of 1 rad/s is 1.
Conclusion
The correct answer is option 'A' - 1. The gain of the system at a frequency of 1 rad/s is 1.
The open loop transfer function of a unity gain negative feedback system is given as
The Nyquist contour in the ��-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
The open loop transfer function of a unity gain negative feedback system is given as
The Nyquist contour in the ��-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to
The Nyquist contour in the ��-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to
a)
0
b)
1
c)
2
d)
3
 | Zoya Sharma answered |
Concept
N = P - 2
N = no. of encirclements of )-1, 0) critical point by the Nyquist plot.
P = no. of right half of s-plane of G(s) H(s) as F(s)
z = no. of lright half of s-plane of CLTF as zero of F(s)
For stability z = 0
N - P = 0
N = P
for Nyquist stability criteria
Calculation
Open loop function:
Close loop transfer function =
Close loop transfer function =
no pole in right hand side
z = 0, P ⇒ 1
N = 1 - 0
N = 1
no. of oncirclements N = 1
From the below given Nyquist plot, calculate the number of open-loop poles on the right-hand side of the s-plane for the closed-loop system to be stable.
- a)1
- b)2
- c)0
- d)-1
Correct answer is option 'A'. Can you explain this answer?
From the below given Nyquist plot, calculate the number of open-loop poles on the right-hand side of the s-plane for the closed-loop system to be stable.
a)
1
b)
2
c)
0
d)
-1
 | Ravi Singh answered |
Principle arguments
- It states that if there are “P” poles and “Z” zeroes for a closed, random selected path then the corresponding G(s)H(s) plane encircles the origin with P – Z times.
- Encirclements in s – plane and GH – plane are shown below.
- In GH plane Anti clockwise encirclements are taken as positive and clockwise encirclements are taken as negative.
It is applied to the total RH plane by selecting a closed path with r = ∞
Nyquist stability completely deals with the right half of s – plane.
N(0, 0) = P – Z
N(0, 0): Number of encirclements around critical point (- 1, 0)
N(0, 0) = P – Z
N(0, 0): Number of encirclements around critical point (- 1, 0)
P: Open loop poles
Z: Open-loop zeroes.
Note:
1) To get the Closed-loop stability we require 1 + GH plane but available is GH plane, hence the origin is shifted to “-1” to get the closed-loop stability.
2) To become the system stable there should not be any closed-loop pole in the right of s – plane.
3) The closed-loop pole is the same as that of the zeroes of Characteristic Equation which must be zero in the right. i.e, Z = 0
N = P is the criteria.
Calculation:
From the given Nyquist plot there is one encirclement about ( -1, 0 ) in the Anti-clockwise direction.
So, N = 1
Now to satisfy the stability criteria N should be equal to P.
N = P = 1
So the number of open-loop poles in the Right-hand side of the system is 1.
The gain margin for the system with open loop transfer function G(s) H(s) = G(s) = 2(1 + s) / s2 is- a)8
- b)0
- c)1
- d)-8
Correct answer is option 'B'. Can you explain this answer?
The gain margin for the system with open loop transfer function G(s) H(s) = G(s) = 2(1 + s) / s2 is
a)
8
b)
0
c)
1
d)
-8
 | Mainak Roy answered |
Open Loop Transfer Function:
The open-loop transfer function of a control system is the transfer function obtained by removing the feedback loop from the system. In this case, the open-loop transfer function is given as:
G(s) = 2(1 - s) / s^2
Gain Margin:
The gain margin is a measure of the system's stability and indicates how much the system's gain can be increased before it becomes unstable. It is defined as the amount of gain at the frequency where the phase of the open-loop transfer function is -180 degrees.
Phase of the Open Loop Transfer Function:
To determine the gain margin, we first need to find the frequency at which the phase of the open-loop transfer function is -180 degrees.
The phase of the open-loop transfer function can be calculated as follows:
Phase = angle(2(1 - s) / s^2)
To find the frequency at which the phase is -180 degrees, we set the phase equal to -180 degrees and solve for s:
-180 = angle(2(1 - s) / s^2)
Finding the Gain Margin:
Once we have found the frequency at which the phase is -180 degrees, we can calculate the gain margin.
The gain margin is given by the reciprocal of the magnitude of the open-loop transfer function at the frequency where the phase is -180 degrees:
Gain Margin = 1 / |G(jω)|
where ω is the frequency at which the phase is -180 degrees.
In this case, since the open-loop transfer function is a rational function, we can substitute jω for s to determine the frequency at which the phase is -180 degrees.
By substituting jω for s in the open-loop transfer function G(s), we can calculate the magnitude of G(jω) at the frequency where the phase is -180 degrees:
|G(jω)| = |2(1 - jω) / (jω)^2|
Simplifying this expression, we get:
|G(jω)| = |2(1 - jω) / -ω^2|
To find the gain margin, we substitute -180 degrees for the phase, calculate the magnitude of the open-loop transfer function at that frequency, and take the reciprocal:
Gain Margin = 1 / |G(jω)|
By performing the calculations, we find that the gain margin is 0.
Therefore, the correct answer is option 'B', 0.
The open-loop transfer function of a control system is the transfer function obtained by removing the feedback loop from the system. In this case, the open-loop transfer function is given as:
G(s) = 2(1 - s) / s^2
Gain Margin:
The gain margin is a measure of the system's stability and indicates how much the system's gain can be increased before it becomes unstable. It is defined as the amount of gain at the frequency where the phase of the open-loop transfer function is -180 degrees.
Phase of the Open Loop Transfer Function:
To determine the gain margin, we first need to find the frequency at which the phase of the open-loop transfer function is -180 degrees.
The phase of the open-loop transfer function can be calculated as follows:
Phase = angle(2(1 - s) / s^2)
To find the frequency at which the phase is -180 degrees, we set the phase equal to -180 degrees and solve for s:
-180 = angle(2(1 - s) / s^2)
Finding the Gain Margin:
Once we have found the frequency at which the phase is -180 degrees, we can calculate the gain margin.
The gain margin is given by the reciprocal of the magnitude of the open-loop transfer function at the frequency where the phase is -180 degrees:
Gain Margin = 1 / |G(jω)|
where ω is the frequency at which the phase is -180 degrees.
In this case, since the open-loop transfer function is a rational function, we can substitute jω for s to determine the frequency at which the phase is -180 degrees.
By substituting jω for s in the open-loop transfer function G(s), we can calculate the magnitude of G(jω) at the frequency where the phase is -180 degrees:
|G(jω)| = |2(1 - jω) / (jω)^2|
Simplifying this expression, we get:
|G(jω)| = |2(1 - jω) / -ω^2|
To find the gain margin, we substitute -180 degrees for the phase, calculate the magnitude of the open-loop transfer function at that frequency, and take the reciprocal:
Gain Margin = 1 / |G(jω)|
By performing the calculations, we find that the gain margin is 0.
Therefore, the correct answer is option 'B', 0.
If the Nyquist plot cuts the negative real axis at a distance of 0.25, then the gain margin and phase margin of the system will be respectively- a)0.25 and 0°
- b)4.0 and -180°
- c)-0.25 and 180°
- d)4.0 and 0°
Correct answer is option 'D'. Can you explain this answer?
If the Nyquist plot cuts the negative real axis at a distance of 0.25, then the gain margin and phase margin of the system will be respectively
a)
0.25 and 0°
b)
4.0 and -180°
c)
-0.25 and 180°
d)
4.0 and 0°
 | Gayatri Menon answered |
Here,
| X | = 0.25 (Given)
∴
Also,
| X | = 0.25 (Given)
∴
Also,
If the gain of the open-loop system is increased to four times, the gain margin of the system- a)remains same
- b)becomes half
- c)becomes one-fourth
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
If the gain of the open-loop system is increased to four times, the gain margin of the system
a)
remains same
b)
becomes half
c)
becomes one-fourth
d)
none of the above
| | Saumya Sen answered |
∴ When open-loop gain becomes 4-times, GM will become one-fourth.
All the constant N-circles in G planes cross the real axis at the fixed points. Which are these points?- a)-1 and origin
- b)Origin and +1
- c)-0.5 and 0.5
- d)-1 and +1
Correct answer is option 'A'. Can you explain this answer?
All the constant N-circles in G planes cross the real axis at the fixed points. Which are these points?
a)
-1 and origin
b)
Origin and +1
c)
-0.5 and 0.5
d)
-1 and +1
 | Sarita Yadav answered |
Centre of N circle is (-1/2, 1/2N)
N = tanα
Constant –N circles always pass through (-1, 0) and (0, 0).
N = tanα
Constant –N circles always pass through (-1, 0) and (0, 0).
The polar plot of a transfer function with ω as the parameter is known as the- a)Nyquist plot
- b)Bode plot
- c)Root-locus
- d)Signal flow graph
Correct answer is option 'A'. Can you explain this answer?
The polar plot of a transfer function with ω as the parameter is known as the
a)
Nyquist plot
b)
Bode plot
c)
Root-locus
d)
Signal flow graph
| | Sarita Yadav answered |
Nyquist plot:
Nyquist plots are an extension of polar plots for finding the stability of the closed-loop control systems. This is done by varying ω from −∞ to ∞, i.e. Nyquist plots are used to draw the complete frequency response of the open-loop transfer function.
Method of drawing Nyquist plot:
Nyquist plots are an extension of polar plots for finding the stability of the closed-loop control systems. This is done by varying ω from −∞ to ∞, i.e. Nyquist plots are used to draw the complete frequency response of the open-loop transfer function.
Method of drawing Nyquist plot:
- Locate the poles and zeros of open-loop transfer function G(s)H(s) in ‘s’ plane.
- Draw the polar plot by varying ω from zero to infinity.
- Draw the mirror image of the above polar plot for values of ω ranging from −∞ to zero.
- The number of infinite radii half circles will be equal to the number of poles at the origin.
- The infinite radius half-circle will start at the point where the mirror image of the polar plot ends. And this infinite radius half-circle will end at the point where the polar plot starts.
Consider the following statements:
Nichol’s chart gives information about.
i. Closed loop frequency response.
ii. The value of the peak magnitude of the closed loop frequency response Mp.
iii. The frequency at which Mp occurs.
Which of the above statements are correct?- a)2 and 3
- b)1 and 2
- c)1 and 3
- d)1,2 and 3
Correct answer is option 'D'. Can you explain this answer?
Consider the following statements:
Nichol’s chart gives information about.
i. Closed loop frequency response.
ii. The value of the peak magnitude of the closed loop frequency response Mp.
iii. The frequency at which Mp occurs.
Which of the above statements are correct?
Nichol’s chart gives information about.
i. Closed loop frequency response.
ii. The value of the peak magnitude of the closed loop frequency response Mp.
iii. The frequency at which Mp occurs.
Which of the above statements are correct?
a)
2 and 3
b)
1 and 2
c)
1 and 3
d)
1,2 and 3
 | Tanya Chauhan answered |
Understanding Nichol's Chart
Nichol's chart is a powerful tool used in control systems to analyze the stability and performance of a closed-loop system. It effectively combines the concepts of frequency response and gain/phase margins, making it an essential component in control engineering.
Correctness of Statements
All three statements provided regarding Nichol's chart are indeed correct. Here’s a detailed explanation:
i. Closed Loop Frequency Response
- Nichol's chart represents the closed-loop frequency response of a control system.
- It illustrates how the output of the system responds to different frequency inputs, providing insight into stability and performance.
ii. Peak Magnitude of Closed Loop Frequency Response (Mp)
- The chart allows engineers to determine the peak magnitude (Mp) of the closed-loop frequency response.
- This peak magnitude indicates the maximum amplification that the system can achieve at a particular frequency before reaching instability.
iii. Frequency at Which Mp Occurs
- Nichol's chart also helps in identifying the specific frequency at which the peak magnitude (Mp) occurs.
- This is crucial for tuning control parameters to optimize system performance and ensure stability.
Conclusion
In summary, Nichol's chart provides comprehensive information about:
- The closed-loop frequency response
- The value of the peak magnitude (Mp)
- The frequency at which Mp occurs
Thus, the correct answer is indeed option 'D', as all three statements accurately describe the capabilities of Nichol's chart in control system analysis.
Nichol's chart is a powerful tool used in control systems to analyze the stability and performance of a closed-loop system. It effectively combines the concepts of frequency response and gain/phase margins, making it an essential component in control engineering.
Correctness of Statements
All three statements provided regarding Nichol's chart are indeed correct. Here’s a detailed explanation:
i. Closed Loop Frequency Response
- Nichol's chart represents the closed-loop frequency response of a control system.
- It illustrates how the output of the system responds to different frequency inputs, providing insight into stability and performance.
ii. Peak Magnitude of Closed Loop Frequency Response (Mp)
- The chart allows engineers to determine the peak magnitude (Mp) of the closed-loop frequency response.
- This peak magnitude indicates the maximum amplification that the system can achieve at a particular frequency before reaching instability.
iii. Frequency at Which Mp Occurs
- Nichol's chart also helps in identifying the specific frequency at which the peak magnitude (Mp) occurs.
- This is crucial for tuning control parameters to optimize system performance and ensure stability.
Conclusion
In summary, Nichol's chart provides comprehensive information about:
- The closed-loop frequency response
- The value of the peak magnitude (Mp)
- The frequency at which Mp occurs
Thus, the correct answer is indeed option 'D', as all three statements accurately describe the capabilities of Nichol's chart in control system analysis.
What is the value of M for the constant M circle represented by the equation 8x2 + 18x + 8y2 + 9 = 0?- a)0.5
- b)2
- c)3
- d)8
Correct answer is option 'C'. Can you explain this answer?
What is the value of M for the constant M circle represented by the equation 8x2 + 18x + 8y2 + 9 = 0?
a)
0.5
b)
2
c)
3
d)
8
| | Sarita Yadav answered |
Comparing with the M circle equation we have the value of M = 3.
Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0?- a)-45°
- b)-60°
- c)-90°
- d)-180°
Correct answer is option 'C'. Can you explain this answer?
Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0?
a)
-45°
b)
-60°
c)
-90°
d)
-180°
| | Zoya Sharma answered |
Addition of pole causes instability to the system.
Consider the system represented by the equation given below. What would be the total phase value at ω = 0?
200/[s3 (s + 3) (s + 6) (s + 10)].- a)-90°
- b)-180°
- c)-270°
- d)-360°
Correct answer is option 'C'. Can you explain this answer?
Consider the system represented by the equation given below. What would be the total phase value at ω = 0?
200/[s3 (s + 3) (s + 6) (s + 10)].
200/[s3 (s + 3) (s + 6) (s + 10)].
a)
-90°
b)
-180°
c)
-270°
d)
-360°
| | Zoya Sharma answered |
The phase can be calculated by the basic formula for calculating phase angle.
Consider the following statements related to frequency domain analysis:
1. The cut-off rate is the slope of the log magnitude curve near the cut-off frequency.
2. The bandwidth is defined as the band of frequencies lying between 3 dB points.
3. Higher the value of resonant frequency of the system, slower is the time response.
4. The magnitude of resonant peak gives the information about the relative stability of the system.
Which of these statements is/are not correct?- a)1,3 and 4
- b)1, 2 and 3
- c)2 and 3
- d)3 and 4
Correct answer is option 'C'. Can you explain this answer?
Consider the following statements related to frequency domain analysis:
1. The cut-off rate is the slope of the log magnitude curve near the cut-off frequency.
2. The bandwidth is defined as the band of frequencies lying between 3 dB points.
3. Higher the value of resonant frequency of the system, slower is the time response.
4. The magnitude of resonant peak gives the information about the relative stability of the system.
Which of these statements is/are not correct?
1. The cut-off rate is the slope of the log magnitude curve near the cut-off frequency.
2. The bandwidth is defined as the band of frequencies lying between 3 dB points.
3. Higher the value of resonant frequency of the system, slower is the time response.
4. The magnitude of resonant peak gives the information about the relative stability of the system.
Which of these statements is/are not correct?
a)
1,3 and 4
b)
1, 2 and 3
c)
2 and 3
d)
3 and 4
 | Megha Datta answered |
The bandwidth is defined as the band of frequencies tying between -3 dB points. Hence, statement-2 is false.
Higher the value of resonant frequency of the system, faster is the time response. Hence, statement-3 is false.
Higher the value of resonant frequency of the system, faster is the time response. Hence, statement-3 is false.
The constant M-circle represented by the equation x2 + 2.25x + y2 = -1.25 has the value of M equal to:- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
The constant M-circle represented by the equation x2 + 2.25x + y2 = -1.25 has the value of M equal to:
a)
1
b)
2
c)
3
d)
4
 | Akshay Nair answered |
Given equation:
The given equation is x^2 + 2.25x + y^2 = -1.25.
Equation of a circle:
The equation of a circle with center (h, k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2.
Comparing the given equation with the equation of a circle:
Comparing the given equation with (x-h)^2 + (y-k)^2 = r^2, we can rewrite the given equation as:
(x+1.125)^2 + (y-0)^2 = (1.25)^2.
So, the center of the circle is (-1.125, 0) and the radius is 1.25.
Radius and diameter:
The radius of a circle is the distance from the center of the circle to any point on the circumference. The diameter of a circle is twice the radius.
In this case, the radius of the circle is 1.25 units. Therefore, the diameter is 2 * 1.25 = 2.5 units.
Constant M:
The constant M in the equation represents the diameter of the circle.
Calculating M:
In the given equation, the value of M can be found by calculating the diameter of the circle.
The equation x^2 + 2.25x + y^2 = -1.25 represents a circle with a diameter of 2.5 units.
Therefore, the value of M is 2.5 units.
Answer:
The value of M in the equation x^2 + 2.25x + y^2 = -1.25 is 2.5 units.
Since none of the given options match the value of M = 2.5, the correct answer cannot be determined from the given options.
The given equation is x^2 + 2.25x + y^2 = -1.25.
Equation of a circle:
The equation of a circle with center (h, k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2.
Comparing the given equation with the equation of a circle:
Comparing the given equation with (x-h)^2 + (y-k)^2 = r^2, we can rewrite the given equation as:
(x+1.125)^2 + (y-0)^2 = (1.25)^2.
So, the center of the circle is (-1.125, 0) and the radius is 1.25.
Radius and diameter:
The radius of a circle is the distance from the center of the circle to any point on the circumference. The diameter of a circle is twice the radius.
In this case, the radius of the circle is 1.25 units. Therefore, the diameter is 2 * 1.25 = 2.5 units.
Constant M:
The constant M in the equation represents the diameter of the circle.
Calculating M:
In the given equation, the value of M can be found by calculating the diameter of the circle.
The equation x^2 + 2.25x + y^2 = -1.25 represents a circle with a diameter of 2.5 units.
Therefore, the value of M is 2.5 units.
Answer:
The value of M in the equation x^2 + 2.25x + y^2 = -1.25 is 2.5 units.
Since none of the given options match the value of M = 2.5, the correct answer cannot be determined from the given options.
Polar plot of G(s) = 
is a- a)straight line
- b)semicircle
- c)parabola
- d)circle
Correct answer is option 'B'. Can you explain this answer?
Polar plot of G(s) = is a
is aa)
straight line
b)
semicircle
c)
parabola
d)
circle
 | Jyoti Basak answered |
Given, 
It is a type - 0 and order - 1 system, therefore its polar-plot will be as shown below.
Hence, the polar plot will be semicircular in shape.
It is a type - 0 and order - 1 system, therefore its polar-plot will be as shown below.
Hence, the polar plot will be semicircular in shape.
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