Question

Direction: It consists of two statements, one labelled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:

Statement (I): At breakaway point the system is critically damped.

Statement (II): At the point where root loci intersect with the imaginary axis, the system is marginally stable.
1. Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true

Answer 1

Correct Answer - Option 2 : Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I)

Root Locus Diagram:

• This method is a graphical technique which gives the position of the roots of the characteristic equation i.e. the position of closed loop poles as the gain K is varied.
• The root locus diagram is plotted by using the open-loop poles but not the closed loop poles.
• If the root loci intersect with the imaginary axis, it indicates that there are roots on imaginary axis and hence the system is marginally stable.
• At a real breakaway point, the system is critically damped as the roots are real and equal.

 

Therefore, both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I)