Question

What do you understand by alternating current (AC.)? Obtain an expression for mean value and root mean square (r.m.s.) value of A.C.

Answer 1

Alternating current : A coil rotated in an uniform magnetic field. The induced e.m.f. is produced. In one revolution the value of e.m.f. is zero and maximum in two times. During first half rotation of the coil, current flows in one direction and in next half rotation of direction is reversed. Its magnitude also changes continuously.

Such a current is called "Alternating Current." 

Thus alternating current varies as sine curve. Hence this is called sinusiodal alternating current. 

A.C. in time t is given by 

where i_o is the maximum current and ω is the angular velocity of coil.

Mean value of A.C.: Average value of alternating current in half time period of rotation of coil is called "mean value of

A.C. (i_m) t is

Root Mean Square (R.M.S) value of A.C.: R.M.S value of A.C. is equal to the square root of the mean of square of current in fully time period of rotation of coil.

It is denoted by i_r.m.s. It is also called 'virtual current.'

Now A.C. at time t = i_o sin ωt dt