Question

A pressure sensor measures 44 psi just before the sudden change of 70 psi. The sensor measures 52 psi at a time 4.5 sec after the change. The sensor time constant (in sec) is

• A. 37

Answer 1

The correct option is A 37
$P_{initial}=44psi$

$P(t=4.5sec)=52psi$

$P_{final}=P_{initial}+70=114psi$

We know the relation
$P\left(t\right)=P_{final}+(P_{initial}-P_{final})e^{-t/\tau }$

$P(t=4.5sec)=114+(44-114)e^{-4.5/\tau }$

$52=114+(-70)e^{-4.5/\tau }$

$\frac{62}{70}=e^{-4.5/\tau }$

$\ell n\left(\frac{62}{70}\right)=\frac{-4.5}{\tau }$

$\tau =\frac{-4.5}{\ell n\left(\frac{62}{70}\right)}$

$\tau =37sec$