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Dimensions in equations

Discussion in 'Electrical Engineering' started by sert, Nov 3, 2007.

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  1. sert

    sert Guest

    I'm reading from an electrical engineering book that some
    voltage v(t) is given by:

    v(t) = sin(1000*t)

    where t is the time

    Isn't this expression, strictly speaking, incorrect? How can we
    find the sine of a time quantity? Shouldn't we have a constant
    in there as well with T^-1 dimension to solve this?

    For example:

    v(t) = sin(1000*k*t)

    where k a constant with units 1/s.
     
  2. Palindrome

    Palindrome Guest


    Personally, balancing units in equations has proven to be one of the
    most useful things that I have ever been taught.
     
  3. Uncle Al

    Uncle Al Guest

    v(t) = v(max)sin(diddle with radians/time)

    Units are consistent.
     
  4. Don Kelly

    Don Kelly Guest

    ----------------------------
    As Salmon egg says sin(1000t) is fine where the 1000 means 1000
    radians/second or 159+ Hz. This gives you sin (quantity in radians) which
    is correct. Dimensionally a radian is T^-1
    Note that the expression should read v(t)=Vmax*sin(1000t) where Vmax is in
    volts (apparently 1V in this case) if you are worried about dimensional
    analysis.
    Possibly you missed something earlier in the book.
     
  5. sert

    sert Guest

    Radians are dimensionless. You were probably thinking of radians
    per second.
     
  6. Don Kelly

    Don Kelly Guest

    ----------------------------
    My goof- Thank you.
     
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