ECE 16.201 Circuit Theory I Recitation Session. Handout #19 –December 5, 2011. Second Order RLC Circuits: After Switching: The circuit contains one Inductor, one capacitor and one equivalent resistance (RLC) Circuit We will study two cases: 1‐ Source free Series RLC 2‐ Step Response Series RLC Circuit Note: The solution to RLC circuits is a second order differential equation, so we need two initial conditions. Hint: If the RLC circuit are connected in series, then solve for IL(t) first, and then solve for anything else in the circuit. ( Initial Conditions are easily obtained. How to Obtain Initial Conditions: 1‐ Draw the circuit before switching (t<0) a. Short the inductor and open the capacitor b. Solve for VC(0) and IL(0) 2‐ Draw the Circuit right after Switching. (t=0+) a. Force VC(0) and IL(0). b. Solve for IC(0+) and VL(0+) c. Since 
d. Also,

Ahmed Abu‐Hajar & Tingshu Hu 1 | P a g e ECE 16.201 Circuit Theory I Recitation Session. Handout #19 –December 5, 2011. Example: 0.5
8Ω 1Ω 0.01F 12V and
a. Solve for VC(0), IL(0), Ahmed Abu‐Hajar & Tingshu Hu 2 | P a g e ECE 16.201 Circuit Theory I Recitation Session. Handout #19 –December 5, 2011. Unit step Response of Series RLC Circuit and √
Three solutions depending on α & ωo 1‐ Overdamped Case (α > ωo) The General solution of the overdamped case: ∞ Steps 1‐ Recognize the circuit is RLC Series Circuit. 2‐ Obtain Initial conditions 3‐ Find IL(∞). 4‐ Find α and ωo. 5‐ If the it is overdamped case: Solve for A1 and A2 of the general solution. Example: Solve for IL(t) 1H i (t)
L
5Ω 2Ω 12V 4Ω 12V 0.25F Ahmed Abu‐Hajar & Tingshu Hu 3 | P a g e ECE 16.201 Circuit Theory I Recitation Session. Handout #19 –December 5, 2011. Solution: Ahmed Abu‐Hajar & Tingshu Hu 4 | P a g e