The response of a series R-C circuit is given by\(I\left( s \right) = \frac{{\frac{{2V}}{\pi } - \frac{{{q_0}}}{C}}}{{R\left( {s + \frac{1}{{RC}}} \right)}}\)Where q0 is the initial charge on the capacitor. What is the final value of the current?

Concept:Final value THEOREM:A final value theorem allows the time domain behaviour to be directly calculated by taking a limit of a frequency domain expressionFinal value theorem states that the final value of a system can be calculated by\(F\left( \infty \right) = \mathop {\lim }\limits_{s \to 0} sF\left( s \right)\)Where F(s) is the Laplace transform of the function.For final value theorem to be applicable system should be stable in steady-state and for that real part of poles should lie in the left side of s plane.Initial value theorem:\(C\left( 0 \right) = \mathop {\lim }\limits_{t \to 0} c\left( t \right) = \mathop {\lim }\limits_{s \to \infty } sC\left( s \right)\)It is applicable only when the NUMBER of poles of C(s) is more than the number of zeros of C(s).Calculation:Given that, \(I\left( s \right) = \FRAC{{\frac{{2V}}{\pi } - \frac{{{q_0}}}{C}}}{{R\left( {s + \frac{1}{{RC}}} \right)}}\)By using final value theorem\(I\left( \infty \right) = \mathop {\lim }\limits_{s \to 0} sI\left( s \right) = \mathop {\lim }\limits_{s \to 0} s\frac{{\frac{{2V}}{\pi } - \frac{{{q_0}}}{C}}}{{R\left( {s + \frac{1}{{RC}}} \right)}} = 0\)