# Determine epsilon naught using a variable capacitor

• Hircine
In summary, the conversation discusses a design for a simple experiment using a variable parallel plate capacitor to measure the value of epsilon naught. One possible solution suggested is using a Wheatstone bridge circuit or a digital multimeter with capacitance measurement function instead of connecting a large number of resistors in series.
Hircine

## Homework Statement

Design a simple experiment using a variable parallel plate capacitor to measure the value of epsilon naught

## Homework Equations

C=(ε0*A)/d Where C is capacitance, A is the area of the plates, and d is the distance between the plates.

## The Attempt at a Solution

So, I hooked up my variable capacitor in series with a variable resistor and a 3V power source. I hooked up the terminals of a voltage probe to the capacitor (one on either plate) to measure the voltage between them. In the circuit, I also had a three-way switch so I could charge the capacitor when the switch was in one position (current going from power source -> resistor -> capacitor -> power source) and then discharge when the switch is in another position (current going from capacitor -> resistor -> capacitor). Now, I'm not sure if you lads and lasses are familiar with a program called LoggerPro or not, but I used that and hooked the voltage probes to my computer so I could generate a graph of voltage versus time. From the graph I can determine the time constant (RC) of the capacitor. I then need to take that, divide by the resistance that I set with the variable resistor to get the capacitance. I can measure the distance between the plates and the area of the plates so I can calculate epsilon naught.

Now for the problem: I googled the model of the variable resistor and it has a range of 0 farads to 225 picofarads. In order to get this idea to work, I'll need 11 billion ohms (since the capacitance is ridiculously small). The largest resistor I have access to is 4.7 mega-ohms.

Now the question: Is there an easier way to do this without having to connect ~2340 of these resistors in series?

Sorry if this is awfully long-winded. I can clarify anything if need be.

Thank you for sharing your experiment design with us. It seems like a good approach to measure the value of epsilon naught using a variable parallel plate capacitor. However, as you have mentioned, using 2340 resistors in series may not be the most practical solution.

One alternative approach could be to use a Wheatstone bridge circuit. This circuit is commonly used to measure unknown resistance values and can also be used to measure capacitance values. You can set up the circuit with a known capacitor in one arm and the variable capacitor in another arm. By adjusting the variable resistor, you can balance the bridge and determine the capacitance value of the unknown capacitor. This value can then be used to calculate the value of epsilon naught.

Another option could be to use a digital multimeter with a capacitance measurement function. This would eliminate the need for a variable resistor and allow for a more accurate measurement of the capacitance value.

I hope these suggestions are helpful in finding a simpler solution for your experiment. Good luck!

## 1. What is epsilon naught?

Epsilon naught, also known as the permittivity of free space, is a physical constant that represents the ability of a vacuum to store an electric field.

## 2. How is epsilon naught related to a variable capacitor?

Epsilon naught is directly related to the capacitance of a variable capacitor, which is a component used in electronic circuits to store electric charge. The capacitance of a variable capacitor changes depending on the distance between its plates, and epsilon naught is used to calculate this change.

## 3. Can epsilon naught be determined experimentally?

Yes, epsilon naught can be determined experimentally by measuring the capacitance of a variable capacitor at different plate distances and using the formula C = ε0A/d, where C is the capacitance, A is the area of the plates, and d is the distance between the plates.

## 4. What units is epsilon naught measured in?

Epsilon naught is typically measured in farads per meter (F/m) or picofarads per meter (pF/m).

## 5. Why is it important to determine epsilon naught using a variable capacitor?

Determining epsilon naught using a variable capacitor is important for understanding the properties of electric fields and for designing and optimizing electronic circuits. It also allows for the accurate calculation of capacitance values in various applications.

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