Question

Determine the rms value of a semi-circular current wave which has a maximum value of $a$.

• A. $\left(1/\sqrt{2}\right)a$
• B. $\sqrt{\left(3/2\right)}a$
• C. $\sqrt{\left(2/3\right)}a$
• D. $\left(1/\sqrt{3}\right)a$

Answer 1

The correct option is A $\left(1/\sqrt{2}\right)a$

The root-mean-square for a current is defined by $I_{rms}=\sqrt{{\left(I^2\right)}_{avg}}$

When this process is carried out for a sinusoidal current, then

$I\left(t\right)=I_{max}sin\left(\omega t\right)=asin\left(\omega t\right)$

$I_{avg}^2=\frac{{\int }_0^{\frac{T}{2}}\left[a^2{sin}^2\right(\omega t\left)\right]}{\frac{T}{2}}=\frac{a^2}{2}$

Taking square root:

$\therefore I_{rms}=\frac{1}{\sqrt{2}}a$