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A resistance of 20 Omega is connected to...

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

A

`0.2 s`

B

`0.25s`

C

`25 s`

D

`2.5 xx 10^(-3)s`

Text Solution

Verified by Experts

The correct Answer is:
D
Both B and I are is same phase. So, let us calculate the time taken by the voltage to change from peak value of rms value.
Now, `220=220 sin 100 pi t_(1)`
or `100 pit_(1)=(pi)/(2) or t_(1)=1/(200)s`
Again, `(200)/(sqrt(2))=200 sin 100 pit_(2)`
or, `1/sqrt(2)=sin 100 pi t_(2) or 100 pi t_(2)=(pi)/(4)`
or `t_(2)=1/400 s`
Required time `=t_(1)-t_(2)`
`=1/200 - 1/400 =(2-1)/(400) = (1)/(400)s=2.5 xx 10^(-3)s`.
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