Question

The period of a sinusoidal source is the time required for the sinusoid to pass through all of its possible values. We use the symbol T to represent the period of a sinusoid. The period and the frequency are inversely related. A sinusoidal source described by the function cos(ωt) has a frequency of ω radians/second, or a frequency f=ω/2π Hz. The units hertz represents the number of cycles per second. Since the period is the number of seconds per cycle, the period is the inverse of the frequency in hertz: T=1f Substituting the frequency in radians/second, ω, for the frequency in Hz gives us another way to calculate the period: T=2πω What is the period of the voltage source described as v(t)=50cos(2000t−45∘) mV? Express your answer to two digits after the decimal point and include the appropriate units.

Answer 1

Answer:

T=0.0031secs

Explanation:

The voltage expression $v(t)=50cos(2000t-45^{0})$ can be represented as

$v(t)=v_{m}cos(wt-\alpha )$

comparing the two equations we can conclude that the angular frequency  

$w=2000$

from the question, since the frequency,f which is express as

$f=\frac{w}{2\pi }$,

Hence  $f=\frac{2000}{2\pi } \\f=\frac{2000}{2*3.14 } \\f=318.471Hz$.

The period which is the inverse of the frequency can be express as

$T=\frac{1}{f} \\T=\frac{1}{314.471}\\ T=0.00314\\T=0.0031secs$