The RLC series circuit is shown below consists of a resistor, capacitor, and inductor in series with a voltage source. R

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The Rlc Series Circuit Is Shown Below Consists Of A Resistor Capacitor And Inductor In Series With A Voltage Source R 1 (45.37 KiB) Viewed 29 times

The RLC series circuit is shown below consists of a resistor, capacitor, and inductor in series with a voltage source. R w C #t Uc ட 00000 (a) Use KVL and the component equations to derive the system model for vcſt). Show all steps of the derivation. (b) Let z1 = ve and z2 = 21. Decompose the system into two first order differential equa- tions. (c) Write the equations as a state space system in matrix form with states z1 and 22. Clearly a show the [A] and matrices. (hint: vs(t) is the system input) (d) Write the output equation with the first output yı as the capacitor voltage ve, the second output y2 as the current in the loop i, and the third output y3 as the resistor voltage Up.