An alternating current is represented by the equation  I = 20 sin 100 ㄫt. Compute its frequency and the maximum and RMS values of current. (Ans :50 Hz, 20 A , 14 A )


Data Given:

I = 20 sin (100ㄫt)


To Find:

(i) Frequency = f = ?

(ii) Maximum Current = `\I_0` = ?

(iii) Root Mean Square (rms) current = `\I_{rms}` = ?


Solution:

General formula for instantaneous current

I = `\I_0` sin ယ t --------------(1)

Given Formula

I = 20 sin 100 ㄫt  ------------(2)


(i) Frequency = f = ?

By Comparing both equations (1) and (2) we have the following values


Angular frequency = ယ = 100 ㄫt  rad s⁻¹

But ယ =  2ㄫf  So,

2ㄫf  = 100 ㄫ  rad s⁻¹

or

f = 50 Hz ---------------Ans. 1


(ii) Maximum Current = `\I_0` = ?

By Comparing both equations (1) and (2) we get


Maximum Current = `\I_0` = 20 A -----------Ans.2



(iii) Root Mean Square (rms) current = `\I_{rms}` = ?

The equation for Root Mean Square (rms) current  `\I_{rms}` is

`\I_{rms}` = `\frac {I_0}{sqrt 2}`

putting values

`\I_{rms}` = `\frac {20 A}{sqrt 2}`

`\I_{rms}` = `\frac {20 A}{1.414}`

`\I_{rms}` = 14.14 A---------------Ans(3)



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