Finding Capacitance & Inductive Reactance for RLC Circuit in FM Broadcasting

AI Thread Summary
An RLC circuit is essential for tuning into FM broadcasting stations, with specific parameters like resistance (12.0 ohms) and inductance (1.40 µH) impacting the required capacitance for resonance at 99.7 MHz. The challenge lies in calculating capacitance without knowing the capacitive reactance (XC), despite having formulas for inductive reactance (XL). Additionally, when a sinusoidal voltage of 120V is applied to an inductor with a peak current of 3.0A, the effects of doubling the frequency on maximum current and inductive reactance need to be analyzed. Understanding the relationship between resonant frequency, inductance, and capacitance is crucial, as well as the role of impedance in the circuit. The discussion highlights the complexity of RLC circuit calculations and the need for clarity in applying relevant equations.
dagg3r
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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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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.
 
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-
 

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