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First_Order_Circuits

First_Order_Circuits - First Order Circuits RC and RL...

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Page 1 of 3 First Order Circuits: RC and RL Circuits Circuits that contain energy storage elements are solved using differential equations. The “order” of the circuit is specified by the order of the differential equation that solves it. A zero order circuit has zero energy storage elements. (Called a “purely resistive” circuit.) The equations that solve it are zero-order differential equations. (i.e. purely algebraic.) A first order circuit has one (irreducible) energy storage element. The equations that solve it are first order differential equations. A second order circuit has two (irreducible) energy storage elements. The equations that solve it are second order differential equations. etc. Let’s consider a circuit with just one capacitor or one inductor, i.e. a first order circuit . By Thevenin’s and Norton’s Theorems we can always reduce a first order circuit to one of these: 𝑑𝑑𝑑𝑑 ( 𝑡𝑡 ) 𝑑𝑑𝑡𝑡 + 𝑑𝑑 ( 𝑡𝑡 ) 𝑅𝑅𝑅𝑅 = 𝑑𝑑 𝑠𝑠 ( 𝑡𝑡 ) 𝑅𝑅𝑅𝑅 𝑑𝑑𝑑𝑑 ( 𝑡𝑡 ) 𝑑𝑑𝑡𝑡 +
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