Finding Capacitance & Inductive Reactance for RLC Circuit in FM Broadcasting

In summary, in the first conversation, the question asks what capacitance should be used in an RLC circuit used for tuning into an FM broadcasting station at 99.7 Mhz, with a resistance of 12.0 ohm and inductance of 1.40 uH. The suggested solution is to use XC=1/wC where C is capacitance, and w=2*pi*f, but it cannot be calculated without Xc. In the second conversation, there is no clear solution for determining the maximum current or inductive reactance at different frequencies. However, there is a relationship between resonant frequency f, inductance L, and capacitance C, and resistance is a type of impedance.
  • #1
dagg3r
67
0
1.
A RLC circuit is used in a radio to tune into an FM broadcasting station at 99.7 Mhz. The resistance in the circuit is 12.0 ohm, and the inductance is 1.40 uH (micro Henry) what capacitance should be used?

this question is tricky what i tried to do is used XC=1/wC where C is capacitance, and w=2*pi*f
and XL=WL i can find Xl since we have the inductance,
but cannot calculate Capacitance since we don't have Xc...
any suggestions?


2. an inductor is connected to a sinusoidal voltage with amplitude of 120V. A peak current of 3.0A appears in the inductor.

a)what is the maximum current if the frequency of the applid voltage is douled
b) what is the inductive reactance at each of the two frequencies?

i have no idea how to do this... i can only think of I = V/R
 
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  • #2
One uses an RLC circuit to tune to a frequency - the resonant frequency.

1.) What is the relationship between the resonant frequency f, inductance L, and capacitance C?

2.) Resistance is a type of impedance, and so is inductance.

Think of the relationship between Voltage, Current and Impedance.
 
  • #3
Hi there, I'm a first year mechatronics student and have come across a problem similar to the OPs question 1.
I have several equations relating to f, L and C but I think the most relevant is: tan(\theta)=((Xl-Xc)/R)
Xl will equal 2*\pi*L but not sure about the tan(\theta) aspect...
Or is it simpler than that and the resistor isn't involved eg, \omega =1/(sqrt(LC))?
Thanks in advance!
M-
 

FAQ: Finding Capacitance & Inductive Reactance for RLC Circuit in FM Broadcasting

1. What is the purpose of finding capacitance and inductive reactance in an RLC circuit for FM broadcasting?

The purpose of finding capacitance and inductive reactance in an RLC (resistor-inductor-capacitor) circuit for FM (frequency modulation) broadcasting is to determine the correct values of these components that will allow the circuit to function optimally. The correct values will ensure that the circuit has the desired frequency response, allowing for clear and stable FM broadcasting.

2. What is capacitance and how does it affect the RLC circuit in FM broadcasting?

Capacitance is the ability of a capacitor to store electrical energy. In an RLC circuit for FM broadcasting, the capacitance value affects the resonant frequency of the circuit. This means that changing the capacitance value will change the frequency at which the circuit can effectively broadcast FM signals.

3. What is inductive reactance and how does it impact the RLC circuit in FM broadcasting?

Inductive reactance is the opposition to the flow of current in an inductor. In an RLC circuit for FM broadcasting, the inductive reactance value affects the bandwidth of the circuit. This means that changing the inductive reactance value will change the range of frequencies that the circuit can effectively broadcast.

4. How do I calculate the capacitance and inductive reactance for an RLC circuit in FM broadcasting?

To calculate the capacitance and inductive reactance for an RLC circuit in FM broadcasting, you will need to use the following formulas:

Capacitance (C) = 1 / (2 * pi * frequency * inductive reactance)

Inductive Reactance (XL) = 2 * pi * frequency * inductance

These formulas take into account the frequency of the FM signal, as well as the inductance and capacitance values of the circuit components.

5. What factors can affect the values of capacitance and inductive reactance in an RLC circuit for FM broadcasting?

The values of capacitance and inductive reactance in an RLC circuit for FM broadcasting can be affected by factors such as the type and quality of the components used, the temperature and humidity of the environment, and the placement of the components within the circuit. It is important to carefully select and test the components to ensure accurate values for optimal FM broadcasting.

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