Alternating Current

Alternating Current

An alternating current (a.c.) is a current which continuously, changes in magnitude and periodically reverses in direction.

i = I₀ sin ωt 

= I₀ sin  t

Here I₀ is the peak value of a.c.

(a) Current, I = I₀ sin ωt

(b) Angular frequency, ω = 2πn   (n is the frequency of a.c.)

(c) I = I₀ sin 2πnt

RMS Value of current and voltage

Given figure indicates an alternating voltage in the form of a sine wave such that at any time, the voltage

where,

If f(t) is a function, then the average value of that function is defined as,

T = time period

Now, the rms value of voltage is defined as the square root of mean of the squares of voltages. So,

T = is the time period

Applying the limits, we get,

Similarly, we get the rms value of ac current,