  The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a
bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the
microelectromechanical systems(MEMS) device with an external pressure term. In
this paper, we classify the behavior of the solution to this equation. We first
show that under certain initial conditions, there exists critical constants
$P^*$ and $\lambda_P^*$ such that when $0\leq P\leq P^*$, $0<\lambda\leq
\lambda_P^*$, there exists a global solution, while for $0\leq P\leq
P^*,\lambda>\lambda_P^*$ or $P>P^*$, the solution quenches in finite time. The
estimate of voltage $\lambda_P^*$, quenching time $T$ and pressure term $P^*$
are investigated. The quenching set $\Sigma$ is proved to be a compact subset
of $\Omega$ with an additional condition, provided $\Omega\subset R^n$ is a
convex bounded set. In particular, if $\Omega$ is radially symmetric, then the
origin is the only quenching point. Furthermore, we not only derive the
two-side bound estimate for the quenching solution, but also study the
asymptotic behavior of the quenching solution in finite time.
