$1.$ Design for transient response.

A spark generator requires a short voltage pulse at $10$ kV $.$ Design an RLC circuit that provides a single voltage pulse to a $\backslash (1\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash )$ load with an amplitude of $10$ kV at $\backslash ($ t$=5\backslash$mu $\backslash$mathrm$\{$~s$\}\backslash )$; the pulse should maintain a voltage of at least $5$ kV for a duration of at least $\backslash (5\backslash$mu $\backslash$mathrm$\{$~s$\}\backslash ).$ Hint: you'll need to include a source to establish initial conditions of stored energy to release in the form of the pulse; you'll likely want to employ a switch or unit step to remove the source when the pulse output is desired.

$3.$ Takeaway Questions:

a$.$ Compare and contrast the Task $1$ application to that of a typical smartphone camera flash.