A sinusoidal voltage is given by the expression ????(????)=20cos(5π×103 ????+60°) V. Determine its (a) frequency in hertz, (b) period in milliseconds, (c) amplitude in volts, and (d) phase angle in degrees

Respuesta :

There are some placeholders in the expression, but they can be safely assumed

Answer:

(a) [tex]f=1617.9\ Hz[/tex]

(b) [tex]T=0.618\ ms[/tex]

(c) [tex]A=20 \ Volts[/tex]

(d) [tex]\varphi=60^o[/tex]

Explanation:

Sinusoidal Waves

An oscillating wave can be expressed as a sinusoidal function as follows

[tex]V(t)&=A\cdot \sin(2\pi ft+\varphi )[/tex]

Where

[tex]A=Amplitude[/tex]

[tex]f=frequency[/tex]

[tex]\varphi=Phase\ angle[/tex]

The voltage of the question is the sinusoid expression  

[tex]V(t)=20cos(5\pi\times 103t+60^o)[/tex]

(a) By comparing with the general formula we have

[tex]f=5\pi\times 103=1617.9\ Hz[/tex]

[tex]\boxed{f=1617.9\ Hz}[/tex]

(b) The period is the reciprocal of the frequency:

[tex]\displaystyle T=\frac{1}{f}[/tex]

[tex]\displaystyle T=\frac{1}{1617.9\ Hz}=0.000618\ sec[/tex]

Converting to milliseconds

[tex]\boxed{T=0.618\ ms}[/tex]

(c) The amplitude is

[tex]\boxed{A=20 \ Volts}[/tex]

(d) Phase angle:

[tex]\boxed{\varphi=60^o}[/tex]