# [Electrical engineering] Second order Parallel RLC Circuits.

• Engineering
• Muskyboi
In summary: And what about the function for the current through the inductor iL(t)?The current through the inductor iL(t) is given by:The current through the inductor iL(t) is given by:
Muskyboi
Homework Statement
Source free Second order Parallel RLC Circuits. How to find functions for inductor current and capacitor voltage with respect to time after current source has been removed?
Relevant Equations
α=1/2RC, w0=(1/lc)^1/2, v(t)=(A1+A2t)e^-αt

The inductor current curve and capacitor voltage curve should look like this after pulling the switch from which the circuit archived a steady state of 1 amp:

The elements share a common voltage, u.

KCL says the sum of all currents = 0.

Form the second-order DE, then solve it.

cnh1995
NascentOxygen said:
The elements share a common voltage, u.

KCL says the sum of all currents = 0.

Form the second-order DE, then solve it.

Can't I just use v(t)=(A1+A2t)e^-αt since the circuit is critically damped (α=w0) and solve for A1 and A2 based upon initial conditions?

Muskyboi said:
Can't I just use v(t)=(A1+A2t)e^-αt since the circuit is critically damped (α=w0) and solve for A1 and A2 based upon initial conditions?
When it's critically damped, that is the way to solve it.

NascentOxygen said:
When it's critically damped, that is the way to solve it.

OK, but How do I find A1 and A2 based upon the initial conditions?

Muskyboi said:
OK, but How do I find A1 and A2 based upon the initial conditions?
You set t=0 in the general solution, and substitute the known initial conditions.

NascentOxygen said:
You set t=0 in the general solution, and substitute the known initial conditions.

A2 is initial current or voltage
to get A1 you must differentiate the equation with respect to time
Find dv/dt or di/dt via KCL or KVL
the dv/dt or di/dt will come from the equation for the capacitor current or inductor voltage (basically ohms law for inductors and capacitors )
now you sub your dv/dt or di/dt into the equation you differentiated with respect to time

My functions for iL(t) and vc(t) have the exact same curves as the simulation:

Your equation for v(x) agrees with what I arrived at.

NascentOxygen said:
Your equation for v(x) agrees with what I arrived at.

And what about the function for the current through the inductor iL(t)?

## 1. What is the purpose of a second order parallel RLC circuit?

A second order parallel RLC circuit is used to filter signals in electronic circuits. It is designed to attenuate or block certain frequencies while allowing others to pass through.

## 2. How does a second order parallel RLC circuit differ from a first order circuit?

A first order circuit only has one reactive element (either an inductor or a capacitor), while a second order circuit has two reactive elements (an inductor and a capacitor) in addition to the resistor. This allows for a steeper roll-off in the frequency response curve.

## 3. What is the significance of the quality factor (Q) in a second order parallel RLC circuit?

The quality factor (Q) is a measure of the selectivity of the circuit, or how well it can filter out unwanted frequencies. A higher Q value indicates a narrower bandwidth and better filtering ability.

## 4. How does the resonant frequency of a second order parallel RLC circuit change as the value of the inductor or capacitor is varied?

The resonant frequency is determined by the values of the inductor and capacitor in the circuit. As the value of either component is increased, the resonant frequency decreases, and vice versa.

## 5. Can a second order parallel RLC circuit be used for amplification?

No, a second order parallel RLC circuit is primarily used for filtering and cannot be used for amplification. However, it can be used in combination with an amplifier to achieve a desired frequency response.

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