# RLC Circuit: Calculate Resonant Frequency, Reactance & Impedence

• k31453
In summary, the conversation is about calculating various values for a RLC series circuit with specific components and an AC source. The resonant frequency, inductive and capacitive reactance, impedance, rms current, and rms voltage across each element at resonance are all calculated. There is a discrepancy between the given values and the values used in the calculation, which may affect the accuracy of the results.
k31453

This is my question 1.

and this is my question 2.

in a RLC series circuit show above are replaced following : R=500Ω L=0.4mH and C=100pF
the circuit is connected to the terminals of an ac source with an rms voltage of 1V, and a variable frequency calculate the following
A) resonant frequency
ans: f = 1/2*pi*sqrt(LC)
= 1/(2*pi*sqrt(0.0004 * 100 * 10^-12)
= 795.77 Khz

b) the inductive and capacitive reactance at resonance
ans: XL = 2*pi*f*L
= 2*pi* 795.775*10^3*0.0004
= 2000 ohm

Xc = 1/(2*pi*f*C)
= 1/(2*pi* 795.775*10^3 * 100 * 10^-12)
= 1999.9998 ohm

C) the impedance at resonance

ans : impedence of resonance is resistance of circuit : z = R = 500 ohm

D) the rms current at resonance
ans: I = V/R = 1/500 = 0.002A

E) the rms voltage across each element at resonance
Ans: Vr = IR
= 0.002 * 500
= 1V

VL = IXL
= 0.002 * 2000
= 4V

Vc = IXc
= 0.002 * 1999.99
= 3.99998 V

So am i doing it right?? because
i got another reply that says this :

Last edited by a moderator:
In your calculation you have used L = 0.4mH but the printed question has L = 0.4H

## 1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) connected in series. It is used to control the flow of electric current and can produce a resonant frequency at which the circuit has maximum energy.

## 2. How do you calculate resonant frequency in an RLC circuit?

The resonant frequency in an RLC circuit can be calculated using the formula: fr = 1 / (2π√(LC)), where fr is the resonant frequency, L is the inductance in henries, and C is the capacitance in farads.

## 3. What is reactance in an RLC circuit?

Reactance is the opposition to the flow of electric current in an RLC circuit caused by the inductor (inductive reactance) or the capacitor (capacitive reactance). It is measured in ohms and can be calculated using the formulas: XL = 2πfL for inductive reactance and XC = 1 / (2πfC) for capacitive reactance.

## 4. How do you calculate impedance in an RLC circuit?

Impedance in an RLC circuit is the total opposition to the flow of electric current, which takes into account both resistance and reactance. It can be calculated using the formula: Z = √(R2 + (XL - XC)2), where Z is the impedance, R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

## 5. How does the resonant frequency affect the behavior of an RLC circuit?

At the resonant frequency, the reactance of the inductor and the capacitor cancel each other out, resulting in the lowest impedance in the circuit. This means that the circuit becomes more efficient in transferring energy and can produce a larger amplitude of current. It also causes the phase shift between voltage and current to be at its minimum, resulting in a purely resistive circuit. This behavior is important in applications such as tuning radio receivers and creating filters in electronic circuits.

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