# Verifying Kirchoff's law in an AC RLC circuit

• Felipe Lincoln
In summary, the oscilloscope picture showed that the peak voltage in each component occurred at different times, and that summing the voltages would not give the same result as summing the individual voltages.
Felipe Lincoln
Gold Member
Poster has been reminded to show their work on the problem in order to get our tutorial help

## Homework Statement

I have the following RLC circuit with an sinusoidal voltage generator and I want to verify the Kirchoff's first law with an oscilloscope. To measure the peak voltage in each of the components I just permute the positions between the component and the resistor.

The question is: If I sum all the peak tension, will I get ##\mathcal{E} = V_R + V_C + V_L## ?
Next question: if I measure each component's voltage with and voltmeter in AC mode, will the result be the same as before?

## The Attempt at a Solution

#### Attachments

• lab1.png
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Hello Felipe,

You'll have to show an attempt at solution -- see guidelines

And list some relevant equations. This way potential helpers cannot distinguish if and how much you know about phase, complex impedance, etcetera.

In the mean time: answers are "No" and "I don't know what you mean with: as before"

Do you do all this on paper or do you have a screen shot of the oscilloscope picture ?
If so, what have you observed ?

Furthermore: 2kHz is a very low frequency compared to the resonance frequency of this circuit, so AC effects are rather small.

I'm almost sure that the answer for my both questions are NO. since the peak voltage does not occur in the same time in the oscilloscope and the AC voltmeter just take the ##1/\sqrt{2}## of the peak voltage it would result the same. Am I right ?

BvU said:
Furthermore: 2kHz is a very low frequency compared to the resonance frequency of this circuit, so AC effects are rather small.
Isn't the resonance frequency ##1/\sqrt{LC} = 2.4~\mathrm{kHz}## ?

How did you calculate that ?

Never mind, I goofed 2.4 kHz it is.

So you have the reactance of the coil, of the capacitor and of the resistor. The voltage (on ch2 of the scope) over the latter gives you the current, so with the 5 V you get the reactance of the RLC series circuit.

You can sum all the peak voltages with ##\mathcal{E} = V_R + V_C + V_L##, but that ##\mathcal{E}## has no physical meaning.

The AC meters usually give you ##V_{\rm eff}## as you indicate, so summing those AC measurements should give you ##\mathcal{E}/\sqrt 2##

In short: I think you understand .

Felipe Lincoln
Yeah, after thinking a bit it already seems quite clear to me. Thank you friend

## 1. What is Kirchoff's law?

Kirchoff's law, also known as Kirchoff's circuit laws, are two fundamental principles in circuit analysis that govern the behavior of electric circuits. They are used to determine the voltage and current in a circuit and are essential for understanding and designing electrical systems.

## 2. How do Kirchoff's laws apply to AC RLC circuits?

Kirchoff's laws apply to all types of circuits, including AC RLC circuits. In these circuits, Kirchoff's current law states that the sum of all currents entering and exiting a node must equal zero, and Kirchoff's voltage law states that the sum of all voltage drops in a closed loop must equal the sum of all voltage rises in that loop.

## 3. What is the purpose of verifying Kirchoff's law in an AC RLC circuit?

The purpose of verifying Kirchoff's law in an AC RLC circuit is to ensure that the circuit is functioning correctly and that the calculations and predictions made using these laws are accurate. It also allows for troubleshooting and identifying any errors or malfunctions in the circuit.

## 4. How can Kirchoff's law be verified in an AC RLC circuit?

Kirchoff's law can be verified in an AC RLC circuit by using a multimeter to measure the voltage and current at various points in the circuit and then applying Kirchoff's laws to calculate the expected values. Any discrepancies between the measured and calculated values indicate a potential error in the circuit.

## 5. Are there any limitations to Kirchoff's laws in AC RLC circuits?

Yes, there are some limitations to Kirchoff's laws in AC RLC circuits. These laws assume ideal circuit components and do not account for non-linear or time-varying elements. They also do not consider the effects of parasitic capacitance and inductance, which can affect the accuracy of the calculations in high-frequency circuits.

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