Second Order Circuits: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
'''Second order circuits''' are circuits that have two energy storage | '''Second order circuits''' are circuits that have two energy storage | ||
elements, resultingin second-order differential equations. | elements, resultingin second-order differential equations. The circuits have to be cast in terms of irreducible elements (i.e. | ||
combine L's and C's into one when possible).[[File:Unforced RLC Circuit.png|thumb|An unforced RLC circuit]] | |||
Consider an un-forced RLC circuit. We want to find <math>V_C</math>. | |||
First, we can use KVL and KCL | |||
<math>V_R + V_L + V_C = 0</math> | |||
<math>iR + L \frac{di}{dt} + V_C = 0</math> | |||
Next, we can use <math>i = C \frac{dV_C}{dt}</math> to get | |||
<math | |||
Revision as of 03:34, 1 March 2024
Second order circuits are circuits that have two energy storage elements, resultingin second-order differential equations. The circuits have to be cast in terms of irreducible elements (i.e.
combine L's and C's into one when possible).
Consider an un-forced RLC circuit. We want to find Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_C} .
First, we can use KVL and KCL
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_R + V_L + V_C = 0}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle iR + L \frac{di}{dt} + V_C = 0}
Next, we can use Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i = C \frac{dV_C}{dt}} to get
<math
