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Question
Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.
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Solution
Frequency of alternating current, f = 50 Hz
Alternation current ( i ) is given by,
i = i0sinωt ...(1)
Here, i0 = peak value of current
Root mean square value of current `(i_rms)` is given by,
`i_{rms } = i_0/ sqrt2 .......(1)`
On substituting the value of the root mean square value of current in place of alternating current in equation (1), we get:
`i_0 / sqrt2 = i_0 sin omega t`
⇒ `1/sqrt2 = sin omega t = sin pi/4`
⇒ t =` pi/(4 omega) = pi/(4xx2pif)` `(therefore (i) = 2pif)`
= `1/(8f) = 1/(8xx50) `
=`1/400 = 0.0025 s`
= 2.5 ms
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