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Q.18 The root locus of a unity feedback system is shown in the figure

1. C(s)/R(s) = K / ((s+1)(s+2))
2. C(s)/R(s) = -K / ((s+1)(s+2)+K)
3. C(s)/R(s) = K / ((s+1)(s+2)-K)
4. C(s)/R(s) = K / ((s+1)(s+2)+K)

Correct answer: C(s)/R(s) = K / ((s+1)(s+2)+K)

Solution

The correct option represents a system where the feedback is negative and the gain K is added to the denominator, which is consistent with the behavior of the root locus as it indicates stability and the movement of poles in the complex plane as K varies.

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