How Do You Convert Voltage to Current in a Pressure Measurement System?

[NeRdHeRd]

Homework Statement

A pressure measurement system uses a sensor that converts pressure into voltage according to the transfer function, Vp = (.5)(square root of P). This voltage is then converted into a current. As pressure varies from 0 - 100 psi, the current varies from 4 - 20 mA.

A. Find the transfer function equation for the conversion of voltage to current.

Known variables
P = 0 - 100 psi
I = 4 - 20 mA2. The attempt at a solution

I would attempt a solution if I knew where to start. The best I can do so far is use the given transfer function of Vp = (.5)(square root of P) to convert pressure into voltage. After that I'm at a loss as to where to get the equation for the conversion of voltage to current. Is there anyone out there that can point me in the right direction?

 

[jhicks]

Yeah that's pretty vague; There is an infinite amount of different functions you can fit to the 2 endpoints given. You can use linear interpolation for the easiest transfer function based on your thinking of grabbing the corresponding voltages to the pressures/currents.

 

[piercas]

Hi there,

I would suggest starting by looking at the relationship between voltage and current. This is known as Ohm's Law, which states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it, and inversely proportional to the resistance (R) of the conductor. Mathematically, this can be expressed as I = V/R.

In your case, the resistance (R) is constant, so we can rewrite this equation as I = kV, where k is a constant. This tells us that the current is directly proportional to the voltage.

Next, we can use the given transfer function to relate voltage to pressure. Since Vp = (.5)(square root of P), we can rewrite this as V = k√P, where k is another constant.

Now, we can combine these two equations to get an equation for the conversion of voltage to current: I = k(k√P) = k^2√P. This means that the current is directly proportional to the square root of the pressure.

To find the value of k, we can use the given values for pressure and current. Plugging in P = 100 psi and I = 20 mA, we get 20 = k^2√100. Solving for k, we get k = 0.2.

Therefore, the transfer function equation for the conversion of voltage to current is I = 0.2√P.

I hope this helps you understand the problem better. If you have any other questions, don't hesitate to ask. Keep up the good work!