Chapter 6-14. RLC Example #14
Recommended Post : 【Circuit Theory】 Chapter 6. RLC Example
1. Problem . RLC Complex Circuit
Figure 1. Problem]
2. Solution
⑴ Case 1. t ＜ 0
Figure 2. Situation when t ＜ 0
① The circuit above is a stable circuit.
○ Meaning : Voltage and current converge.
○ Justification : Consists only of voltage sources.
○ When t = 0-, the inductor can be considered a short circuit, and the capacitor an open circuit.
② Proof
○ The capacitor is at a lower position (ⓐ) in the voltage gradient, so the charge accumulates, but the voltage cannot exceed that of the open-circuited state.
○ The voltage of the capacitor, exceeding the voltage of the open-circuited state, would act like a battery → Contradiction at ⓐ.
○ The capacitor is always stable in a circuit composed only of constant voltage sources.
○ Completeness Axiom : An increasing and bounded function always converges.
③ Initial Conditions
⑵ Case 2. t ＞ 0 : Represented as a matrix, then using Cramer’s rule
Figure 3. Situation when t ＞ 0
Input: 2016.01.18 19:57