Electronics/RCL time domain2

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Figure 1: RCL circuit
Figure 1: RCL circuit

Example:[edit]

Given the following values what is the response of the system when the switch is closed?

R L C V
0.5H 1kΩ 100nF 1V

Solve for and :

From equation \ref{eq:vf}, for a unit step of magnitude 1V. Therefore substitution of and into equation \ref{eq:nonhomogeneous} gives:

for the voltage across the capacitor is zero,

for , the current in the inductor must be zero,

substituting from equation \ref{eq:B1} gives

For , is given by:

is given by:

For , is given by: