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 If k is the duty cycles of the controller, then the rms value of the output voltage in case of a integral cycle control circuit will be?
Consider the input to be sinusoidal with peak value Vm and rms value Vs.
  • a)
    Vs x k
  • b)
    Vs/k
  • c)
    Vs x √k
  • d)
    Vs
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If k is the duty cycles of the controller, then the rms value of the o...
Vrms = [ (k/2π) x ∫Vmsin⁡2 ωt d(ωt) ] 1/2 
Where the integral runs from 0 to 2π.
Vrms = (Vm/√2) k = Vs x √k.
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Most Upvoted Answer
If k is the duty cycles of the controller, then the rms value of the o...
The correct answer is c) Vs x √(k).

In integral cycle control circuit, the output voltage is controlled by turning on and off the power to the load for integral number of cycles. The duty cycle, k, represents the fraction of time the power is turned on.

The output voltage can be calculated by multiplying the input voltage by the duty cycle, k. So, the average output voltage is Vs x k.

However, to calculate the rms value of the output voltage, we need to consider the fact that the power is turned on and off. This results in the output voltage having a higher peak value than the average voltage.

The rms value of the output voltage can be calculated by multiplying the average voltage by the square root of the duty cycle, k. So, the rms value of the output voltage is Vs x √(k).
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