Electro Magnetic Induction And Alternating Currents Question 414
Question: A resistance of 20 $ \Omega $ is connected to a source of an alternating potential V= 220 $ \sin (100\pi t) $ . The time taken by the current to change from the peak value to rms value, is
Options:
A) $ 0.2,s $
B) $ 0.25,s $
C) $ 0.25\times {{10}^{-3}},s $
D) $ 0.25\times {{10}^{-3}},s $
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Answer:
Correct Answer: D
Solution:
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Both V and I are in the same phase.
So, let us calculate the time taken by the voltage to change from peak value to rms value. Now 220 $ \sin 100\pi t_{1} $
Or $ 100\pi t_{1}=\frac{\pi }{2} $
or $ t_{1}=\frac{1}{200}s $ Again, $ \frac{220}{\sqrt{2}}=220\sin 100\pi t_{2} $
Or $ \frac{1}{\sqrt{2}}=\sin 100\pi t_{2} $ or $ 100\pi t_{2}=\frac{3\pi }{4} $
Or $ t_{2}=\frac{3}{400}s $
Required time $ =t_{2}-t_{1}=\frac{1}{400}s=2.5\times {{10}^{-3}}s $
