# Total Current in RLC Parallel Circuit

• aurao2003
In summary, the conversation discusses a question about demonstrating the total current in an RLC parallel circuit with specific component values. The solution involves calculating the individual branch currents and using the total current formula. It is also noted that the complex impedance method would work for this circuit.
aurao2003

## Homework Statement

Hi
Can a kind person please check my solution? This is the question: Demonstrate the total current in an RLC parallel circuit using the following circuit. I can't draw it but the inductive reactance is 20ohms, capacitive reactance is 5ohms and resistor of 10ohms. All are in parallel. The voltage is 5v in series with 20ohms inductive reactance.

## The Attempt at a Solution

This is my attempted solution:
Resistive Branch: I = E/R = 5/10 = 0.5A
Capacitive Branch : E/Xc = 5/5 = 1A
Inductive Branch = E/XL =5/20 = 0.25A
Resultant current, Ix = 1 - 0.25 = 0.75A

Total current = (I^2R + I^2X)^1/2
= (0.75^2 + 0.5^2)^1/2

aurao2003 said:

## Homework Statement

Hi
Can a kind person please check my solution? This is the question: Demonstrate the total current in an RLC parallel circuit using the following circuit. I can't draw it but the inductive reactance is 20ohms, capacitive reactance is 5ohms and resistor of 10ohms. All are in parallel. The voltage is 5v in series with 20ohms inductive reactance.

## The Attempt at a Solution

This is my attempted solution:
Resistive Branch: I = E/R = 5/10 = 0.5A
Capacitive Branch : E/Xc = 5/5 = 1A
Inductive Branch = E/XL =5/20 = 0.25A
Resultant current, Ix = 1 - 0.25 = 0.75A

Total current = (I^2R + I^2X)^1/2
= (0.75^2 + 0.5^2)^1/2

Hello aurao2003.

Is this more or less what your circuit looks like?

I suspect that the question wants to know the value of the current I as produced by the voltage source.

Note that since the inductor is in series with the voltage source there will be a potential drop across that inductor before the current reaches the paralleled R & C.

Do you know how to work with impedances (complex numbers)?

#### Attachments

• Fig1.gif
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Yes. That's what my circuit looks like. I have done complex numbers in my maths class.

Is my solution on track? Please let me know.

aurao2003 said:
Yes. That's what my circuit looks like. I have done complex numbers in my maths class.

Is my solution on track? Please let me know.

Alas, your solution is not "on track" because you have neglected the potential drop that must occur across the inductor -- the total current passes through the inductor before it ever reaches the capacitor or resistor.

Since you have experience with complex numbers, treat the components if they were plain resistors but with values as shown in the diagram I supplied. What would be the total "resistance" as seen by the voltage source? This "resistance" is the circuit's impedance.

You can find the total current if you have the voltage supplied and the impedance. So first find that impedance.

gneill said:
Alas, your solution is not "on track" because you have neglected the potential drop that must occur across the inductor -- the total current passes through the inductor before it ever reaches the capacitor or resistor.

Since you have experience with complex numbers, treat the components if they were plain resistors but with values as shown in the diagram I supplied. What would be the total "resistance" as seen by the voltage source? This "resistance" is the circuit's impedance.

You can find the total current if you have the voltage supplied and the impedance. So first find that impedance.

Thanks for your help. I mislead you about the diagram. The inductor, capacitor and resistor are all in parallel with the supply voltage at the bottom of the circuit. Does this clarify matters? I apologize for not presenting a diagram.

You didn't provide a frequency for the voltage source. Is the voltage DC or AC?

aurao2003 said:
Thanks for your help. I mislead you about the diagram. The inductor, capacitor and resistor are all in parallel with the supply voltage at the bottom of the circuit. Does this clarify matters? I apologize for not presenting a diagram.

Okay, no problem. So the "new" arrangement looks like this:

In this case your original method will work fine. This is because all three passive components are being driven by the same voltage, so you can determine the individual branch currents quite easily. Your answer looks fine.

Note that the complex impedance method would work too (in fact it always works).

#### Attachments

• Fig1.gif
1.6 KB · Views: 568
Last edited:
gneill said:
Okay, no problem. So the "new" arrangement looks like this:

In this case your original method will work fine. This is because all three passive components are being driven by the same voltage, so you can determine the individual branch currents quite easily. Your answer looks fine.

Note that the complex impedance method always would work too (in fact it always works).

Thanks a million. You are amazing! I might some other. Hope it's okay to let you know.

Cheers!

## 1. What is an RLC parallel circuit?

An RLC parallel circuit is a type of circuit that contains a resistor (R), inductor (L), and capacitor (C) connected in parallel. This means that the components are connected side by side, with the same voltage across each component.

## 2. What is the purpose of an RLC parallel circuit?

The purpose of an RLC parallel circuit is to filter out specific frequencies from a signal. The resistor, inductor, and capacitor work together to create a bandpass filter, allowing only certain frequencies to pass through the circuit.

## 3. How does an RLC parallel circuit affect voltage and current?

An RLC parallel circuit affects voltage and current in different ways. The resistor will decrease both voltage and current, the inductor will increase voltage and decrease current, and the capacitor will increase current and decrease voltage. The overall effect on voltage and current will depend on the values of the components and the frequency of the signal.

## 4. What is the resonance frequency of an RLC parallel circuit?

The resonance frequency of an RLC parallel circuit is the frequency at which the inductive and capacitive reactances are equal, resulting in a maximum current and minimum impedance. This frequency is calculated using the formula 1/√(LC), where L is the inductance of the circuit and C is the capacitance.

## 5. What are some real-world applications of RLC parallel circuits?

RLC parallel circuits are commonly used in electronic devices such as radios, televisions, and audio systems to filter out unwanted frequencies and improve signal quality. They are also used in power supplies to regulate voltage and current. Additionally, RLC parallel circuits are used in wireless communication systems and electronic filters.

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