How to get frequency, w (omega), when calculating reactance

In summary, a question was posed regarding finding inductive and capacitive reactance, and the solution sheet specified a frequency of 10000, while the question sheet did not mention a frequency. It was suggested that this may be a typo and the correct frequency should be 1000.
  • #1
KingDaniel
44
1
Hi,
I came across a question from our weekly set of questions that involved finding the inductive reactance and capacitive reactance, ie: XL = jwL and XC = 1 / jwC.
In the solution sheet, the professor wrote that the frequency, w (omega) = 10000, however, in the question sheet, it was nowhere to be found. Is 10000 the standard frequency or is there a way of determining it?
I will upload 2 images of the solution to illustrate my query:
IMG_0623.JPG


IMG_0625.JPG
 
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  • #2
The frequency is specified as is = 6 cos(10^3t) in the form Acos(wt). So I think it might be a typo. I think omega should be 1000, not 10000.
 
  • #3
@analogdesign , Oh yeah, of course. My bad. Thanks
 

1. How do I calculate the frequency, w (omega), for reactance?

To calculate the frequency, w (omega), for reactance, you can use the formula w = 2πf, where f is the frequency in Hertz (Hz). Alternatively, you can use the formula w = 1/RC, where R is the resistance in Ohms and C is the capacitance in Farads.

2. What is the relationship between frequency and reactance?

The relationship between frequency and reactance is inversely proportional. This means that as the frequency increases, the reactance decreases and vice versa. In other words, the higher the frequency, the easier it is for a circuit to allow current to flow through it.

3. Can I calculate reactance without knowing the frequency?

Yes, you can calculate reactance without knowing the frequency by using the formula X = 1/wC, where X is the reactance in Ohms, w is the frequency in radians per second, and C is the capacitance in Farads. This formula works for capacitive reactance (Xc), while for inductive reactance (Xl), you can use the formula X = wL, where L is the inductance in Henrys.

4. How does reactance affect the overall impedance of a circuit?

Reactance is one of the two components of impedance, the other being resistance. The overall impedance of a circuit is affected by both reactance and resistance. In a purely resistive circuit, the impedance is equal to the resistance. However, in circuits with reactive components, the impedance is a combination of both resistance and reactance and is calculated using the formula Z = √(R^2 + X^2), where Z is the impedance, R is the resistance, and X is the reactance.

5. Can I use the same formula to calculate reactance for AC and DC circuits?

No, the formula used to calculate reactance differs for AC and DC circuits. For DC circuits, which have a constant voltage and current, the reactance is zero. For AC circuits, which have a varying voltage and current, the reactance is calculated using the formulas mentioned in the previous questions.

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