Question

RMS value of a current I = 2 sin200πt + 2 cos(200πt + 30°) will be

Answer 1

RMS value of current is √2 A.

we have to find the RMS value of I = 2sin(200πt) + 2cos(200πt + 30°)

first resolve the equation into simpler form,

I = 2sin(200πt) + 2cos(200πt + 30°)

we know, cos(A + B) = cosA.cosB - sinA.sinB

so, cos(200πt + 30°) = cos(200πt).cos30° - sin(200πt).sin30°

= (√3/2)cos(200πt) - (1/2)sin(200πt)

now I = 2sin(200πt) + 2[√3/2 cos(200πt) - (1/2)sin(200πt)]

= 2sin(200πt) + √3cos(200πt) - sin(200πt)

= sin(200πt) + √3cos(200πt)

= 2[1/2sin(200πt) + √3/2 cos(200πt)]

= 2[cos60° sin(200πt) + sin60° cos(200πt)]

= 2sin(200πt + 60°)

so peak value of current is , I_p = 2

now RMS value of current, I_RMS = I_p/√2 = 2/√2 = √2 A