Electro Magnetic Induction And Alternating Currents Question 173

Question: The voltage time (V-t) graph for triangular wave having peak value $ V_{0} $ is as .

The rms value of V in time interval from t=0 to T/4 is

Options:

A) $ \frac{V_{0}}{\sqrt{3}} $

B) $ \frac{V_{0}}{2} $

C) $ \frac{V_{0}}{\sqrt{2}} $

D) $ \frac{V_{0}}{3} $

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Answer:

Correct Answer: A

Solution:

  • $ V=\frac{V_{0}}{T/4}t\Rightarrow V=\frac{4V_{0}}{T}t $
    $ \Rightarrow ,V_{rms}=\sqrt{V^{2}}=\frac{4V_{0}}{T}\sqrt{t} $

$ =\frac{4V_{0}}{T}{ \frac{\int\limits_{0}^{T/4}{t^{2}dt}}{\int\limits_{0}^{T/4}{dt}} }=\frac{V_{0}}{\sqrt{3}} $



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