Understand the question

The question asks for the RMS (Root Mean Square) value of current. RMS value of current is the square root of the mean of the squares of the values of the current.

$\sqrt{\frac{I_1°2 + I_2°2 + \ldots + I_n^2}{n}}$

Relate RMS current to peak current

RMS current is related to the peak current by the formula $I_{rms} = \frac{I_m}{\sqrt{2}}$. This formula is derived by taking the square root of the mean of the squares of the values of the peak current.

$\frac{I_m}{\sqrt{2}}$

Simplify the formula

To simplify the formula, multiply the numerator and denominator by $\sqrt{2}$to get $I_{rms} = \frac{I_m}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{I_m \sqrt{2}}{2}$

$\frac{I_m \sqrt{2}}{2}$

Further simplify the formula

This simplifies further to $\boxed{I_{rms} = 0.707I_m}$. Hence, the RMS value of current is $0.707$ times the peak value.

$0.707I_m$