- #1

Vaclav

- 10

- 1

## Homework Statement

Hello,

In a lab experiment, we wanted to compare the time constant in a simple RC circuit by comparing the value of Resistance * Capacitance that we measure directly and the value of RC that we get from the procedure. The procedure entailed using a wave generator and an oscilloscope to graph the charging and discharging patterns of the capacitor. We did four trials using different capacitors and resistances, but I will only use one as an example to get the idea of what we did across.

So in the we had a single capacitor (with capacitance C = 25.2 nF) and two resistors in series (which we calculate to be R = 245.5 kΩ) that was connected in a loop with the wave generator terminals. The wave generator was set to produce square waves and cause the capacitor to charge and discharge constantly. The oscilloscope terminals were attached to the circuit on each side of the capacitor and after some fine adjusts on the range of voltage and time, a nice charging pattern was produced. In this case, the max voltage reached is 10 volts.

After filming the charging pattern, we plotted some easy to determine points for (t, V) to replicate the curve in Excel. We then graphed the smooth curve that is generated from the theory that the voltage across the capacitor is V = Vo(1 - e^(-t/RC)), where we take Vo to be 10 volts and R and C to be the values that we measured before the experiment began. We were told by our instructor that Vo would be the max values for voltage that your data is heading to, and since a good portion of our graph our data values are nearly at 10V, we take Vo to be 10V.

Our objective is to compare the time constant that our experiment data is indicating to the theoretical time constant we get from measure R and C directly. The resistance R and capacitance C was measured using an multimeter, where R was measured on the ohmmeter setting and the capacitance was measured by first discharging it and then inserting it into slits in the multimeter (for this specific use) and using the capacitance setting. To determine the time constant indicated by our data, we then changed the capacitance C to change the time constant until the curve mapped to the data points.

## Homework Equations

Voltage over a capacitor is: V = Vo(1 - e^(-t/RC))

Equivalent resistance for series resistors: Req = R1 + R2

Time constant (tau): tau = R*C

## The Attempt at a Solution

The theoretical time constant I calculate is R*C = 245.5 kΩ * 25.2 nF = 6.19 ms. However, according to the theoretical curve the time constant must be close to 4.89 ms. To figure out what might be causing this discrepancy I have looked at if any possible error involved in measuring R or C could make the graph be off so much. To get the theoretical curve to map to the data points I either have to decrease C by 5.3 nF or decrease the resistance R by 52 kΩ. Both of these seem seem like impossible errors especially considering that the multimeter should have been able to read accurately 245.x kΩ and 25.x nF, so I figure that there has to be some other factor that is causing the discrepancy, but I cannot figure out what that factor might be.

I have been reading that measuring capacitance is not the easiest thing to do, but our meter seemed to read it just fine. However, maybe this is not a very accurate method? Changing Vo does not make the graph any better either and I doubt the resistances being off by 50kΩ. For the three other trials we did (another single capacitor, two capacitors in series, and two capacitors in parallel), we have the same issue. In all four, the theoretical curve is always lower than the curve indicated by the data points, which I assume is the effect of some issue that happened in all four trials. Any help is greatly appreciated.