Second order circuit need some confirmation on the steps involved.

In summary, the problem involves finding v(t) for all t>0 using a second order method. Before the switch is closed, the current is found to be 0.25A using KCL and KVL equations are used to solve for v(t). The question mentions using a Norton equivalent and the use of Laplace transforms is discussed. The importance of taking into account the dependent source is also mentioned.
  • #1
berry1991
6
0

Homework Statement


Find v(t) for all t>0. Use second order method.


Homework Equations





The Attempt at a Solution


Before the switch is closed:
solving for i:
-80+160i+80i+80i=0
i=0.25A

KCL:
From node v(t):
[C dv(t)/dt] + i(t) + [V(t)/4] + [(v(t)-80i)/80]+[(v(t)-80)/160] = 0

KVL:
v(t)=L di(t)/dt

Later on solve the 1st equation for i(t), then substitute into KVL equation.
 

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  • #2
Consider replacing everything before the switch with a Norton equivalent.

Have you learned about Laplace transforms yet?
 
  • #3
yes, but the question ask us to use 2nd order to solve it.
Do we need to take in account for the dependent source?
we convert it to 80*0.25=20V
 
  • #4
berry1991 said:
yes, but the question ask us to use 2nd order to solve it.
In my opinion, I don't think that using Laplace transforms to solve the differential equation would be cheating...
Do we need to take in account for the dependent source?
we convert it to 80*0.25=20V
Yes, the dependent source makes a difference, but you may be surprised by the resulting Norton equivalent. The Norton equivalent should have a current source in parallel with a resistance; 20V is not a current (nor is the the correct Thevenin voltage).
 
  • #5


The second order method involves using differential equations and circuit analysis techniques to solve for the voltage (v(t)) in a second order circuit. This typically involves using Kirchhoff's laws and the circuit's differential equations to create a system of equations that can be solved for the voltage at any given time (t). The steps involved may vary depending on the specific circuit and its components, but generally involve setting up the equations, solving for the unknown variables (such as i and v(t)), and then using those solutions to find the overall voltage at any given time. It is important to carefully consider the circuit's components and their properties in order to accurately solve the equations and find the correct solution.
 

FAQ: Second order circuit need some confirmation on the steps involved.

What is a second order circuit?

A second order circuit is an electrical circuit that contains at least one capacitor and one inductor, in addition to resistors and voltage/current sources. These circuits have two energy storage elements and exhibit second order differential equations in their behavior.

What are the steps involved in solving a second order circuit?

The steps involved in solving a second order circuit include: identifying the circuit elements, writing Kirchhoff's voltage and current laws for the circuit, determining the differential equation governing the circuit, finding the initial conditions, solving the differential equation, and finally, interpreting and verifying the solution.

How do you solve a second order circuit using Laplace transforms?

To solve a second order circuit using Laplace transforms, you first need to take the Laplace transform of the differential equation governing the circuit. Then, use algebraic manipulation to rearrange the equation into a form that can be solved for the desired variable. Finally, take the inverse Laplace transform to obtain the solution in the time domain.

What is the significance of the natural response in a second order circuit?

The natural response in a second order circuit is the response of the circuit without any external inputs. It is determined by the circuit's initial conditions and the values of its components. The natural response can tell us about the circuit's stability and its behavior over time.

How are the roots of the characteristic equation related to the behavior of a second order circuit?

The roots of the characteristic equation, also known as the poles of the transfer function, determine the behavior of a second order circuit. If the roots are real and negative, the circuit will be stable and exhibit decaying oscillations. If the roots are complex, the circuit will exhibit oscillations that may or may not decay, depending on the damping ratio. If the roots are real and positive, the circuit will be unstable and exhibit growing oscillations.

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