Question

A step voltage V(t) = 100 u(t) is applied to a series RLC circuit with

L=10H, R=2ohm and C= 5F. The initial current in the circuit is zero but

there is an initial voltage of 50V on the capacitor in a direction which

opposes the applied source. Formulate the expressions for the current

in the circuit.

Answer 1

GIven quantities: V(t) = 100 u(t) L = 10H, R = 2ohm and C = 5F $U_o = 50V$

Z = $\sqrt{R^2+(X_L - X_C)^2} = \sqrt{R^2+(wL - \large\frac{1}{wC})^2} = \sqrt {4+(10w - \large\frac{1}{5w})}$

$I = \large\frac{U_o}{Z} = \frac{50\sqrt{5w}}{\sqrt{100w^2+20w-1}}$