# Help with Second Order Circuits

• Engineering
• cshum00
In summary, the conversation is about a RLC circuit in series where the current passing through the circuit needs to be found. The circuit is critically damped and the simplified expression for current is given. The goal is to find the constant A2. The equations and steps to solve the problem are provided, with a mistake identified and corrected using the product rule. The final solution is i(t) = -9.4te-20t.
cshum00

## Homework Statement

I have a RLC circuit in series. I am trying to find the current i(t) passing through this RCL circuit. When solving the RCL circuit, it happened to be critically damped. And simplified i ended up with:
i(t) = A2te-20t
Where i need to find what is the cosntant A2

## Homework Equations

R = 100Ohm
L = 2.5H
C = 1mF
i(0) = 0A
vC(0) = 24V
vL = L di/dt
vR = iR
di/dt = -20A2te-20t

## The Attempt at a Solution

I apply KVL to the closed RCL loop and get:
vC + vL + vR = 0
vC(0) + L di(0)/dt + i(0)R = 0
24V + 2.5H di(0)/dt + 0 = 0
di(0)/dt = -24V/2.5H = -9.4A

But di/dt is also -20A2te-20t so
di(0)/dt = -9.4 = -20A2(0)e-20(0)
-9.4 = 0
which is fallacy

but according to the book:
A2 = -9.4
so,
i(t) = -9.4te-20t

Where did i go wrong?

Dear Friend

di/dt = A2 * t * (-20 * e (-20t) ) + A2 * e(-20t)

The derivative of multiplied terms.

Rgiht! How could i make such a basic mistake. The product rule! Thanks a bunch. T^T

## 1. What is a Second Order Circuit?

A Second Order Circuit is an electrical circuit that contains two energy storage elements, such as capacitors or inductors. These elements can store energy in the form of an electric field (capacitor) or magnetic field (inductor), and their behavior is described by second-order differential equations.

## 2. How do I solve Second Order Circuits?

The most common method for solving Second Order Circuits is by using differential equations. This involves setting up the differential equations for the circuit using Kirchhoff's laws and then solving them using techniques such as Laplace transforms or series solutions.

## 3. What is the time constant of a Second Order Circuit?

The time constant of a Second Order Circuit is the time it takes for the system to reach 63.2% of its steady-state value. It is determined by the values of the circuit's components, such as resistors, capacitors, and inductors.

## 4. Can I use circuit analysis software to solve Second Order Circuits?

Yes, there are various circuit analysis software programs available that can solve Second Order Circuits. These programs use numerical methods to solve the differential equations and provide graphical representations of the circuit's behavior.

## 5. How do I determine the stability of a Second Order Circuit?

The stability of a Second Order Circuit can be determined by analyzing its transfer function. If the poles of the transfer function lie on the left half of the complex plane, the circuit is stable. If they lie on the right half, the circuit is unstable. Additionally, the location of the poles can also indicate the type of response the circuit will have, such as overdamped, underdamped, or critically damped.

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