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Question

A resistance of 20 Ω is connected to a source of alternating current rated 110 V,50 Hz. Find the time taken by the current to change from its first maximum value to the consecutive rms value.

A
5.5 ms
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B
4.5 ms
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C
2.5 ms
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D
3.5 ms
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Solution

The correct option is C 2.5 ms
Let the current be, i=i0sinωt.

Also, let t1 and t2 be the time instants for consecutive appearances of the maximum value and the rms value of the current, respectively.

i0=i0sinωt1

ωt1=π2t1=π2ω

i02=i0sinωt2

ωt2=3π4t2=3π4ω [As we are taking the rms value after the first peak value]

So, the time taken by the current to change from its first maximum value to the consecutive rms value is,

t2t1=3π4ωπ2ω=π4ω

t2t1=π4(2πf)=18×50=2.5×103 s=2.5 ms

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