Question
The current through a resistor in an a.c circuit is given as 2sinωt. Determine the d.c equivalent of the current.
Solution
The equation given to us is 2sinωt and the peak current, Io = 2A
The direct current (d.c) equivalent of the current is the root mean square (Irms)value of the current.
Irms = Io / √2 = 2/√2 = (2/√2) x (√2/√2) = (2/√2)/√4 = (2√2)/2 = √2A
Therefore, the root mean square value of the current is √2 Ampere.