# Homework Help: Units of constant of proportionality, can I sum them like this ?

1. May 22, 2012

### gjenn01

1. The problem statement, all variables and given/known data
Hello,

I have four different, but known, dimensionless values C1, C2, C3 and C4 (they are actually contrasts that can be displayed on a crt monitor).

I have measured the voltages (V1 and V2) required to produce C1 and C2 in isolation, but have had to measure V3 by combining C3 and C4 together, I think I may have the relationsihps as defined below, where a and b are scaling constants, and also there is a relation between C1 and C3 and also C2 and C4, hence the use of the same scaling fators.

2. Relevant equations

V1 = a * C1
V2 = b * C2, and
V3 = (a * C3) + (b * C4)

3. The attempt at a solution

My question is can I simply say that I'm going to define a and b to have the units of Volts in order for the equtions to balance? and in the case of V3 can I just sum the products a*C3 and b*C4 and set it equal to V3?

I think this is a valid method of combining units, but would be grateful for any advice if I have overlooked something or made a logical error, etc, many thanks.

Last edited: May 22, 2012