What is the value of ω for a RLC AC circuit with given parameters?

[musiliu]

Homework Statement

I am given a RLC circuit with a AC power source (e.g. signal generator), and i want to find the reactance of the capacitor.

Given: R = 2200 Ohms, L = .025 H, C = (1 x 10^-9) F, V₀ = 5 V
f = 3000 Hz

Homework Equations

edit: Sorry i wrote wrong formula.. here is the correct one:

Reactance of Capacitor = 1 / ω C

The Attempt at a Solution

I know how to solve this problem, but i am not sure what value to use for ω.

My teacher refers to ω as the "frequency", but isn't it supposed to be ω = 2 pi f ?

So, simply put, am i supposed to use the 3000 Hz as my ω, or do i use 2 pi f as my ω?

 

[kuruman]

Use ω = 2 π f. Also there is no V₀ in the reactance.

 

[musiliu]

i learned that ω is the angular frequency.. so am i supposed to use ω = 2 pi f for this problem? i am confused since my teacher keeps calling ω the frequency and not the angular frequency...

 

[kuruman]

i learned that ω is the angular frequency.. so am i supposed to use ω = 2 pi f for this problem? i am confused since my teacher keeps calling ω the frequency and not the angular frequency...

It is a bit confusing at first because your teacher is cutting corners. You can tell whether one is talking about ω or about f by looking at the units. When you see rad/s (or s^-1), it is ω. When you see Hz (or cycles per second), it is f.

 

[rwisz]

As a scientist, it is important to use the correct values and equations in your calculations. In this case, you are correct that ω is typically defined as 2πf, where f is the frequency in Hz. So, in this problem, you would use ω = 2π(3000 Hz) = 18849.56 radians/second.

It is also important to note that the reactance of a capacitor is frequency-dependent, so it is important to use the correct value for ω in your calculations to get an accurate result. Using the wrong value for ω could lead to incorrect conclusions about the behavior of the RLC circuit.

In summary, always use the correct equations and values in your calculations to ensure accurate and reliable results.