Electronics Engineering (ELEX) Board Practice Exam

In a root locus, how many branches will tend towards infinity if the number of poles equals the number of zeroes?

1. 1

2. 2

3. 0

4. Infinite

The correct answer is: 0

In a root locus analysis, the number of branches that tend towards infinity is determined by the difference between the number of poles and the number of zeros in a system. When the number of poles is equal to the number of zeros, it means that all the poles can be canceled out by the zeros as we approach infinity in the s-plane. As a result, there will be no branches that extend to infinity because every pole has a corresponding zero to counteract its effect. This leads to a stable system where all roots (or poles) are accounted for within the finite area of the s-plane. Thus, the correct understanding is that with equal numbers of poles and zeros, there will be zero branches that tend towards infinity in the root locus plot. Hence, the answer is accurate.