Question

The rms value of current i = 10 + 5 cos (628t + 30) is

Answer 1

The rms value of current i=10+5cos(628t+30) is $\frac{15}{\sqrt{2} }$

• The effective rms value of the given instantaneous current is a combination of DC and AC
• Now squaring both sides we get i^2 = 100 + 25cos^2(628t+30) + 100cos(628t+30)
• Using a trigonometric identity we get i^2 = 100 + (25/2)(1+cos(1256t+60)) + 100cos(628t+30)
• Upon simplification it becomes  $\frac{225}{2}$ + (25/2)cos(1256t+60) + 100cos(628t + 30)

• Now we have to take the average value. Now the average values of cosines are 0. Hence we can ignore these terms. So we left only the average of $\frac{225}{2}$

• As this is a constant then the average has the same value. So finally applying square root operation we get $\frac{15}{\sqrt{2} }$

• So the required rms value is $\frac{15}{\sqrt{2} }$