# RLC circuits and Phasors

#### Azez

Joined Jan 16, 2012
13
Hi,

I'm stuck on a few minor things in my coursework that I just need straightening out if anyone can help!!!

1. When doing an analysis of Rlc circuits, what is the voltage response? I've looked on the web and in notes but it talks about frequency response etc but not voltage response.

2. How do you convert things into phasor form? Or notation. I have Acos(ωt +θ) but that's where I get stuck. The value to convert is 8cos(t+∏/4)v. So I'm not quite sure how to kinda fit the numerical values into the equation, do you then also have to convert the values of the resistors and capacitors as well?

Sorry I know it's 2 separate questions in one post, I just didn't want to smiling up the forum with too many posts!

Any help would be really appreciated Thank you!

#### t_n_k

Joined Mar 6, 2009
5,455
1. From the perspective of terminology it's quite reasonable in many situations to consider the voltage response and frequency response to be closely related. Take the case of an amplifier driven by a variable frequency voltage source and where the desired amplifier output is also a voltage signal. The frequency response would be the ratio of the output and input voltages for the range of frequencies of interest. So in that instance the frequency response is related to voltage signals but is actually a dimensionless value - since it is based on a ratio.

2. If the time domain function is v(t)=Acos(ωt+θ)=8cos(t+∏/4) [volts]

As a phasor in the frequency domain one would normally write this as

$$\vec{V}=A\angle{\theta}=8\angle{45^o}$$

• Azez

#### Azez

Joined Jan 16, 2012
13

1. The question itself asks 'Use differential equations to calculate the voltage response for the network. Assume zero initial conditions. State if the current is under-damped, critically damped or over-damped.' I have everything I need for the damping however it is the voltage response for the RLC circuit. I've attached the network drawing below (sorry shouldve done this first!

2. Do I apply the phasor equation to all the variables ie the resistor values etc or just the 8cos(t+∏/4)?

#### t_n_k

Joined Mar 6, 2009
5,455
There's no AC voltage source shown in the circuit. Where are you getting the 8cos(t+pi/4) from? The source shown is a simple step function.

#### Azez

Joined Jan 16, 2012
13
Sorry about that! The 8cos(t-π/4) came from a separate question from the voltage response.

I apologise for not being clearer, I'm new to the forums and I didn't want to continually post about help so I kinda put 2 questions in 1 thread.

The second question with the phasors in is: