Electro Magnetic Induction And Alternating Currents Question 173
The voltage time (V-t) graph for a 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} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ V=\frac{V_{0}}{T/4}t\Rightarrow V=\frac{4V_{0}}{T}t $
$ \Rightarrow ,V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T} V^{2} dt}=\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}}{2} $
BETA
