Alternating Current (A.C.)

Topic Content:

An alternating current (A.C.) is a current that varies in magnitude over time, sinusoidally, in such a way as to reverse its direction periodically, i.e. It is a current that flows in the positive and negative direction periodically.

Equation of A.C. Current:

An a.c is represented by:

⇒ \( \scriptsize I = I_o \: sin \:2 \pi f t \\ \scriptsize = I_o \: sin \:2 \omega t \)

• I = instantaneous current 
• f = frequency 
• ωt = phase angle of the current
• ω = 2πf = angular velocity 
• I_o = maximum or peak current 

Also, alternating voltage is:

⇒ \(\scriptsize V = V_o \: sin \:2 \pi f t \\ \scriptsize = V_o \: sin \:2 \omega t \)

Instantaneous current is the amount of charge passing through a conductor at a specific moment in time, whereas the time-averaged current is the total amount of charge passing through a conductor in a time interval.

Example 6.2.1:

An a.c. voltage is represented by the equation, V = 4Sin900πt.
Calculate the:

(i) the peak voltage.
(ii) the frequency.
(iii) the angular velocity.

Solution:

You have to compare the given equation to the general equation:

The general equation is ⇒ \(\scriptsize V = V_o \: sin \:2 \pi f t \)

The