# Determine epsilon naught using a variable capacitor

## 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.