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Solved Problems-6

Problems-6
A series R-L-C circuit with R = 3Ω, L = 1H and C = 0.5 F is excited with a unit step voltage. Obtain an expression for the current, using Laplace transform. Assume that the circuit is relaxed initially.
Solution
By KVL,
Description: Description: 7405.png
 
Since the circuit is initially relaxed,
∴ Description: Description: 7414.png
 
Putting the values,
Description: Description: 7420.png
 
or I(s) = Description: Description: 7433.png
 
where, Description: Description: 7439.png
 
∴ Description: Description: 7445.png
 
Taking inverse Laplace transform,
i(t) = e t + e–2t (A)
 
Description: Description: 7451.png 
 




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