Question

The root locus approaches straight lines as asymptotes approaches

• A. Zero
• B. Unity
• C. Infinity
• D. \(j\omega\) axis

Hint:

Number of asymptotes: \[ N_a=n-m \] Angle of asymptotes: \[ \theta=\frac{(2q+1)180^\circ}{n-m} \] where \(q=0,1,2,\dots\)

Answer 1

The Correct Option is C

Concept: In root locus analysis, asymptotes describe the behavior of branches that extend toward infinity. They indicate the direction of root locus branches when the gain \(K\) becomes very large.

Step 1: Recall the meaning of asymptotes.
When the number of poles exceeds the number of zeros, \[ n-m \] branches must terminate at infinity. These branches follow straight-line asymptotes.

Step 2: Interpret the statement.
Root locus branches approach these asymptotes only as \[ K\rightarrow\infty. \] Therefore asymptotes represent the path of roots at infinity.

Step 3: Final conclusion.
\[ \boxed{\text{Root locus approaches straight lines as } s\rightarrow\infty} \] Hence, \[ \boxed{\text{Correct Option (C)}} \]