Laplace transforms: R series with RC parallel circuit

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Problem Statement

Find the Voltage across the capacitor for t>=0:
Voltage across capacitor at t({0-})=0
Fig (1)















Use Loop Equations to solve for the currents in and


Loop 1
_______________________________________equation (1)


Loop 2
_______________________equation (2)


Solve equations (1) and (2) simultaneously


Substituting equation (1) into equation (2) gives...
simplifies to...


Take the Laplace Transform to move to the S-domain





Take the inverse Laplace transform to move back into the t-domain


substitute this equation back into equation (1)


Voltage on Capacitor


Answer:

Volts



Written by: Andrew Hellie

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