How Do You Analyze a Second Order RLC Circuit for Different Responses?

[mspruill]

Second Order RLC CIrcuit?

Homework Statement

for this figure, v_in(t) = -250u(-t) + 750U(t) mV, R = 0.5 ohms, L = 1 H, C = 0.01 F.
Find zero-input, zero state, and complete response of both V_c(t) and I_L(t) for t>0.

Homework Equations

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The Attempt at a Solution

I found the i_L (0⁺) = 0 and V_c(0⁺) = -125

From here I'm stuck

 

[KataKoniK]

...

Hi there,

The circuit you are referring to is called a second order RLC circuit. This type of circuit is commonly used in many electronic devices, such as filters and oscillators.

To find the zero-input response of Vc(t) and IL(t), you will need to use the initial conditions you have already calculated (iL(0+) = 0 and Vc(0+) = -125) and solve the differential equations for the circuit.

The zero-state response can be found by setting the input voltage to 0 and solving the differential equations again.

The complete response is the sum of the zero-input and zero-state responses.

I hope this helps. Let me know if you have any further questions. Good luck with your homework!

 

[Mene]

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I would approach this problem by first understanding the components and behavior of a second order RLC (resistor-inductor-capacitor) circuit. This type of circuit is characterized by a second order differential equation that describes the relationship between voltage, current, and time.

In this case, the circuit consists of a resistor (R), an inductor (L), and a capacitor (C), connected in series with a voltage source (vin(t)). The voltage across the capacitor (Vc) and the current through the inductor (IL) will vary over time as the circuit reaches a steady state.

To solve for the zero-input response, we can assume that the initial conditions (iL(0+) and Vc(0+)) are both zero. This means that there is no initial energy stored in the inductor or capacitor. We can then use the differential equation for the circuit to find the steady state values of Vc and IL.

To find the zero-state response, we need to consider the effects of the input voltage on the circuit. In this case, the input voltage has two parts: a negative step function (-250u(-t)) and a positive step function (750U(t)). We can use the Laplace transform to solve for the response of the circuit to each of these input functions, and then add them together to get the complete response.

Overall, the solution to this problem involves using mathematical methods to solve the differential equation for the circuit and considering the effects of the input voltage. It is important to carefully consider the initial conditions and the behavior of the circuit components to accurately solve for the responses of Vc and IL.