# Dimensions in equations

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

1. ### sertGuest

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. ### PalindromeGuest

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

3. ### Uncle AlGuest

Units are consistent.

4. ### Don KellyGuest

----------------------------
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.