A sinusoidal A .C . has a maximum value of 15 A. What are its RMS values? If the time is recorded from the instant the current is zero and is becoming positive, what is the instantaneous value of the current after 1/300 s? given the frequency is 50 Hz. (Ans: `I_{rms}` = 10 .6 A, Instantaneous current = 13.0 A ) 



Data Given:

Maximum Current = `\I_0` =  15 A

Time = t = `\frac {1}{300}` s

Frequency = f = 50 Hz



To Find:

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

(ii) Instantaneous Current = I = ?


e="background-color: white; color: black;">(i) 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 {15 A}{sqrt 2}`

`\I_{rms}` = `\frac {15 A}{1.414}`

`\I_{rms}` = 10.6 A---------------Ans(1)



(ii) Instantaneous Current = I = ?


The formula for the instantaneous value of current  I is

I = `\I_0` sin ယ t

where ယ = 2ㄫf , So

I = `\I_0` sin 2ã„«f t

putting values

I = 15 A ï½˜ sin (2ㄫｘ 50 Hz ï½˜ `\frac {1}{300}`s) 

I = 15 A ï½˜ sin (`\frac {ã„«}{3}`) 

I = 15 A ï½˜ sin (`\frac {ã„«}{3}`) 

[ `\frac {ã„«}{3}` = 60° ] So, 

I = 15 A ï½˜ sin (60°) 

I = 15 A ï½˜ 0.866

I = 12.990 A

or

I = 13 A ----------------Ans. (2)




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