A pressure sensor has a 155 ms time constant and an output o

A pressure sensor has a 155 ms time constant and an output of Vp = 0.55[p] 1/2 where p is the pressure in psi. At t = 0 the input changes suddenly from 20 psi to 200 psi. What is the sensor output voltage at 100 ms?

Solution

Time constant of prressure sensor T=155 ms

Output Voltage Final value Vp=0.55*(p)^1/2 V

Output Voltage including time constant and function of time given as Vp(t)=0.55*(p)^1/2*(1-e^(-t/155ms) V

At t=0 input chnages from 20 psi to 200psi ouptput voltage is

Vp(t)=0.55*(20)^1/2 +0.55*(200-20)^1/2*(1-e^(-t/155ms) V

because the input is 20psi before t=0 so it has voltage corresponding to it before and additional increase of 180 psi

is given that is added to the previous voltage with time constant

Now to find voltage at t=100 ms substitute value in Vp(t)

Vp(t=100ms)=0.55*(20)^1/2 +0.55*(200-20)^1/2*(1-e^(-100ms/155ms) V

Vp(t=100ms)=25.9931 V

SO OUTPUT VOLTAGE AT T=100 ms is Vp=25.99 V