Question

The RMS (root mean square) value of current is related to peak current i_m by ______.

Options

• I = 2 i_m​

• I = \[\frac{i_m}{\sqrt{2}}\approx0.707i_m\]

• I = \[\frac {i_m}{2}\]

• I = \[\sqrt 2\]i_m

Answer 1

The RMS (root mean square) value of current is related to peak current i_m by I = \[\frac{i_m}{\sqrt{2}}\approx0.707i_m\].

Explanation:

The rms current is derived from the average of i² over a full cycle. Using (sin⁡²ωt) = \[\frac {1}{2}\]​, we get I = \[\frac {i_m}{\sqrt 2}\] = 0.707 i_m​. This is the effective DC-equivalent current.