Calculate the instantaneous value at 60° , average value and RMS valu

1.	Calculate the instantaneous value at 60° , average value and RMS value of an alternating current whose peak value is 20 A.
Answer» Peak value of current, I = 20 A Angle, θ = 60° [θ = ωt] (i) Instantaneous value of current, i = l_msin ωt = I_m sin θ = 20 sin 60° = 20 x \(\frac{\sqrt 3}{2}\) = 10√3 = 10 x 1.732 i = 17.32 A (ii) Average value of current, l_av= \(\frac{2I_m}{π}\) = \(\frac{2 \times 20}{3.14}\) (iii) RMS value of current, I_RMS= 0.707 I_m or \(\frac{I_m}{\sqrt2}\) = 0.707 x 20 I_RMS = 14.14 A

Calculate the instantaneous value at 60° , average value and RMS value of an alternating current whose peak value is 20 A.

Answer»

Peak value of current, I = 20 A

Angle, θ = 60° [θ = ωt]

(i) Instantaneous value of current,

i = l_msin ωt = I_m sin θ

= 20 sin 60° = 20 x \(\frac{\sqrt 3}{2}\) = 10√3 = 10 x 1.732

i = 17.32 A

(ii) Average value of current,

l_av= \(\frac{2I_m}{π}\) = \(\frac{2 \times 20}{3.14}\)

(iii) RMS value of current,

I_RMS= 0.707 I_m

or \(\frac{I_m}{\sqrt2}\) = 0.707 x 20

I_RMS = 14.14 A

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Calculate the instantaneous value at 60° , average value and RMS value of an alternating current whose peak value is 20 A.

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