Voltages and currents that vary symmetrically in magnitude and direction with time are very common.
The electric mains supply in our homes and offices is a voltage that varies like a sine function with time.
Such a voltage is called alternating voltage (ac voltage) and the current driven through the appliances is
called the alternating current (ac current).

`text(Basic Principle of AC Generation:)`

Alternating voltage is generated by rotating a coil of conducting wire in a strong magnetic fie ld. The
magnetic flux linked with the coil changes with time and an alternating emf is thus induced. Instantaneous
flux linked with coil is

`phi = (vecA.vecB)n`

`= ABncos(wt+theta_0)`

where A= area of the coil (in `m^2`)
B = magnetic field (in tesla)
n = number of tums
w = angular frequency =`2pi/T`=`2pif` (in rad `s^-1`)
f= frequency (in hertz)
`theta_0` = initial phase angle

With the change of time `cos( wt +theta_0)` changes consequently an emf V is induced. According to Faraday's law

`V = (dphi)/(dt)`

`= (d[(ABncos(omegat+theta_0)))] /(dt)`

`= ABnwsin(omegat+theta_0)`

`V = V_m sin(omegat +theta_0)`

`V_m =` voltage amplitude of sinusoidal voltage or the peak value of ac voltage
where `V_m = ABnomega`