An alternating current i is given by:

i(t) = 141.4 sin 400πt A. Find the time period of the current.

Concept:

Considered a sinusoidal Alternating wave of voltage and current

From the waveform:

And,

Where Vm and Im are the maximum value of instantaneous voltage and current respectively.

v, i is the instantaneous value of voltage and current at any instant t.

ω is the angular frequency in radian/second.

And, ω = 2πf  

f is the frequency in Hz

ϕ is the phase difference between voltage and current

From the above three equations instantaneous value of voltage and current can be written as: is

And,

Calculation:

Sinusoidal wave is given as,

i(t) = 141.4 sin 400πt A.

Comparing to the given equation

∴ f = 200 Hz

We know that,