Solving State Variable Equations With zero input, a series RLC circuit can be described by the following coupled first-order equations in the inductor current iL(t) and capacitor voltage vC(t).

dvCðtÞ

dt

¼ 1 C

iLðtÞ

diLðtÞ

dt

¼  1 L

vCðtÞ  R L

iLðtÞ

(a) Transform these equations into the s domain and solve for the transforms IL(s) and vC(s) in terms of the initial conditions iL(0) ¼ I0 and vC(0) ¼ V0.

(b) Find iL(t) and vC(t) for R ¼ 1 kV, L ¼ 1 H, C ¼ 1 mF, I0 ¼ 15 mA and v0 ¼ 10 V.