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An AC voltage is given by v(t) = 5 + sin(2000πt), what is the time period and the dc component in v(t)?
  • a)
    0.05 ms, 0V
  • b)
    1 ms, 0V
  • c)
    0.05 ms, 5V
  • d)
    1 ms, 5V
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
An AC voltage is given by v(t) = 5 + sin(2000πt), what is the time ...
Concept
For a DC signal
  • The average value over one time period is non zero
  • The non-zero value is known as the DC value
  • 'A 'is the DC component of the signal
Calculation
Given the signal v(t) = 5 + sin(2000πt)
Now 
we have, 
The average value of sinusoidal signal over one time period is always 0
Hence the DC component of the signal v(t) is 5
Now observe the AC component in signal v(t)
sin(2000πt) is the AC component
The angular frequency ω = 2000π 
Also ω = 2π / T ; here T is the Time period of the signal
2π / T= 2000π
T = 10-3 s 
T =1 ms
The Time period of the signal is 1 ms
Therefore the correct answer is option 4
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Community Answer
An AC voltage is given by v(t) = 5 + sin(2000πt), what is the time ...
The AC voltage given by v(t) = 5 sin(2000t) has an amplitude of 5 volts and a frequency of 2000 Hz. The time variable, t, represents time in seconds.
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