Units of constant of proportionality, can I sum them like this ?

[gjenn01]

Homework Statement

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.

Homework Equations

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

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.

 

[anathema]

Thank you for sharing your question with us. It seems like you are trying to determine the scaling constants a and b in order to calculate the voltage required to produce a certain contrast value on a CRT monitor. Your proposed method of defining a and b with the units of volts and summing the products in the case of V3 seems reasonable.

However, it is important to note that the units of a and b should be determined based on the units of C1, C2, C3, and C4. For example, if C1 is in units of percentage and C2 is in units of decibels, a and b would need to have different units in order for the equations to balance. It would be helpful to provide more information about the units of your contrast values in order to ensure accurate calculations.

Additionally, it may be useful to double check your equations and make sure they accurately reflect the relationships between the contrast values and voltages. If you have any further questions or concerns, please don't hesitate to ask. Good luck with your research!