Question #161479

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.

Expert's answer

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\n{4+(10w - \\large\\frac{1}{5w})}"

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

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