# Calculate RLC Circuit Values: R1, R2, and Xl | Step-by-Step Guide

• Engineering
• ragamuffin_8
In summary: So we work out the angle for each element using its reactance, and the voltage across it using Ohm's law, and THEN add the voltages up. This will give us a voltage, {\color{Red} {V_{RMS}}} , across the entire circuit.
ragamuffin_8

## Homework Statement

An RLC circuits consists of R1 a 10-ohm resistor, R2 a resistor that takes 50 W, C1 a capacitor with 5-ohm reactance, and L1 an inductor that takes 100 var. Find the value of R1, R2, and Xl (inductive reactance).

## Homework Equations

P = (I^2)R
Xc = 1/(2∏fC)
Xl = 2∏fL
Z = √(R^2 + XeqL^2)

## The Attempt at a Solution

I tried equating the currents but I don't know what to do next. I tried to solve for the equivalent impedance but without the frequency of the source, my efforts were futile. Perhaps I could assume a frequency of 60 Hz?

Last edited:
ragamuffin_8 said:

## Homework Statement

An RLC circuits consists of R1 a 10-ohm resistor, R2 a resistor that takes 50 W, C1 a capacitor with 5-ohm reactance, and L1 an inductor that takes 100 var. Find the value of R1, R2, and Xl (inductive reactance).

## Homework Equations

P = (I^2)R
Xc = 1/(2∏fC)
Xl = 2∏fL
Z = √(R^2 + XeqL^2)

## The Attempt at a Solution

I tried equating the currents but I don't know what to do next. I tried to solve for the equivalent impedance but without the frequency of the source, my efforts were futile. Perhaps I could assume a frequency of 60 Hz?

Is this parallel or series RLC?

jegues said:
Is this parallel or series RLC?

I forgot to mention, this is connected in SERIES. I'm sorry

I think we need another clue, such as the line voltage, or that the load has unity power factor.

By assuming a current, I, in all the elements I can find the voltage across each in terms of that I, but that's as far as I can get without more information.

I'm sorry I forgot to mention the line voltage. 100 Vac. But the frequency was not given, how do I start attacking this problem?

ragamuffin_8 said:
I'm sorry I forgot to mention the line voltage. 100 Vac.
Forgot?!

how do I start attacking this problem?

Start by drawing a large schematic, and mark on the quantities you are given for each element.

Assume a branch current, I, and using what you are told about each element, determine the voltage across that particular element in terms of I. The only unknown on the right-hand side of each equation will be I, any other terms on the right-hand side will be known numbers that you can work out from the information provided.

You do not need to know the line frequency.

Good luck!

NascentOxygen said:
Forgot?!

Start by drawing a large schematic, and mark on the quantities you are given for each element.

Assume a branch current, I, and using what you are told about each element, determine the voltage across that particular element in terms of I. The only unknown on the right-hand side of each equation will be I, any other terms on the right-hand side will be known numbers that you can work out from the information provided.

You do not need to know the line frequency.

Good luck!

Thanks Sir NascentOxygen!

I was not thinking of KVL that's why I'm having a hard time in this problem. :shy: I'm sorry

My attempt:

100 V = IR1 + IXc + IR2 + IXL

but:
P = VR2I
VR2 = 50/I

P = I2XL
XL = 100/I2

so:

100 = 10I + 5I + 50/I + 100/I

Solving for I, I got two values I = 4.39 and I = 2.28, which value should I choose?

NascentOxygen said:
Forgot?!

Start by drawing a large schematic, and mark on the quantities you are given for each element.

Assume a branch current, I, and using what you are told about each element, determine the voltage across that particular element in terms of I. The only unknown on the right-hand side of each equation will be I, any other terms on the right-hand side will be known numbers that you can work out from the information provided.

You do not need to know the line frequency.

Good luck!

Thanks Sir NascentOxygen!

I was not thinking of KVL that's why I'm having a hard time in this problem. :shy: I'm sorry

My attempt:

100 = IR1 + IXc + IR2 + IXL

but:
P = VR2I
VR2 = 50/I

P = I2XL
XL = 100/I2

so:

100 = 10I + 5I + 50/I + 100/I

Solving for I, I got two values I = 4.39 and I = 2.28, which value should I choose?

ragamuffin_8 said:
My attempt:

100 = IR1 + IXc + IR2 + IXL
That's a good start, but we distinguish resistance from reactance by associating an angle with reactance. So the equation above needs to be fixed to include this. There are a couple of ways to represent angle, use whichever you like to correct the above equation.

but:
P = VR2I
VR2 = 50/I
yes

P = I2XL
XL = 100/I2
What law did you rely on here?

NascentOxygen said:
That's a good start, but we distinguish resistance from reactance by associating an angle with reactance. So the equation above needs to be fixed to include this. There are a couple of ways to represent angle, use whichever you like to correct the above equation.

I don't quite understand sir. Would you please elaborate?

We write VL for an inductor as ${\color{Blue} {j I X_{L}}} \text{ or as } {\color{Blue}{IX_{L} \angle 90^{\circ}}}\text{ where } X_{L}$ is the magnitude of the inductive reactance.

And something similar for the voltage across a capacitor. Then addition of voltages takes the form of addition of vectors.

## What is a hard RLC series circuit?

A hard RLC series circuit is a type of electrical circuit that consists of a resistor, inductor, and capacitor connected in series. It is called "hard" because the components used in this circuit have high values of resistance, inductance, and capacitance, making it more difficult to analyze and design compared to other types of RLC circuits.

## How does a hard RLC series circuit behave?

The behavior of a hard RLC series circuit is governed by the principles of electrical impedance and resonance. At low frequencies, the inductor dominates the impedance, while at high frequencies, the capacitor dominates. At the resonant frequency, the inductive and capacitive reactances cancel each other out, resulting in a purely resistive impedance.

## What is the formula for calculating the resonant frequency of a hard RLC series circuit?

The resonant frequency of a hard RLC series circuit can be calculated using the formula fr = 1 / (2π√(LC)), where fr is the resonant frequency, L is the inductance, and C is the capacitance.

## How do you calculate the total impedance of a hard RLC series circuit?

The total impedance of a hard RLC series circuit can be calculated using the formula Ztotal = √(R2 + (XL - XC)2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

## What is the significance of the Q factor in a hard RLC series circuit?

The Q factor, also known as the quality factor, is a measure of the sharpness of the resonance in a hard RLC series circuit. It is calculated by dividing the reactance at the resonant frequency by the total resistance in the circuit. A higher Q factor indicates a more selective or tuned circuit, while a lower Q factor indicates a less selective or wider bandwidth circuit.

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