Question

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

Answer 1

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