Impendance in RCL circuit

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In summary, an RLC circuit with a capacitance of 0.26 µF has a resonant frequency of 95 MHz and a corresponding inductance of 10.5712 pH. To calculate the value of R needed for an impedance of 1/5 at resonance compared to 10 kHz, the impedance equation should be solved for R at resonance and set equal to the impedance at 10 kHz. The solution for R is 1.1326 ohms.
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Homework Statement



An RLC circuit has a capacitance of C=0.26 µF.

(a) What inductance will produce a resonant frequency of 95 Mz? -----pH
(b) If the impedance at resonance is 1/5 of the impedance at 10 kHz, what value of R should be chosen? ----Ohm

Homework Equations



omega = 1/(LC)^1/2

Z=[(R^2 + (wL-(1/wC)^2]^1/2



The Attempt at a Solution



Part (a): I used omega = 1/(LC)^1/2, and got the correct answer, 10.5712pH

Part (b): I tried setting the impendane at resonance equal to the impendance at 10kHz and solving for R, but I could not arrive at a solution. So, instead, since Z=R at resonance, I tried solving the impendance equation only at resonace for Z=R, but I have too many unknowns. Can anyone offer a hint as to how I should set this part up? Thanks!
 
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  • #2
Nevermind, math errors. I managed to figure it out.
 
  • #3




In order to solve for the value of R, you can use the given information that the impedance at resonance is 1/5 of the impedance at 10 kHz. This means that at resonance, the impedance is equal to 1/5 of the value of R from the impedance equation. So, you can set up the equation Z=R and substitute 1/5 of R for Z. This will give you a single equation with one unknown, which you can then solve for R.
 

1. What is impendance in an RCL circuit?

Impedance in an RCL circuit is a measure of the overall opposition to the flow of alternating current (AC) caused by the combination of resistance, capacitance, and inductance in the circuit.

2. How is impendance calculated in an RCL circuit?

Impedance is calculated using the formula Z = √(R² + (Xl - Xc)²), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.

3. What is the difference between impendance and resistance in an RCL circuit?

Resistance is the opposition to the flow of current caused by the material the circuit is made of, while impedance is the overall opposition to the flow of AC caused by the combination of resistance, capacitance, and inductance.

4. How does impendance affect the behavior of an RCL circuit?

Impedance affects the behavior of an RCL circuit by determining the flow of current through the circuit. A higher impedance will result in a lower current, while a lower impedance will result in a higher current.

5. What factors can affect the impendance in an RCL circuit?

The impendance in an RCL circuit can be affected by the frequency of the AC source, the values of resistance, capacitance, and inductance in the circuit, and the arrangement of the components in the circuit.

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