6/2/15 - AC Circuits Cont.

Today, we begin by looking at what happens when more elements are in an AC circuit. Particularly the RLC version.

We state that Z is total rectance of the circuit and we find it by the sum of the square of the resistance and the square of the difference of the inductive reactance and capacitive reactance.

Since we don't have an inductor in the circuit, we just have the reactance of the capacitor.

We calculate the theoretical limits of what would happen if certain circuit elements go to infinity.

We say since that is the equation to find current, we say that current should increase or decrease by a factor of 0 < X < 2 since it is bound by the limit.

Here we hook up a resistor and capacitor in series and apply LoggerPro sensors to the circuit.

The voltage probe was in the wrong position, but was later fixed.

Here we have the potential and current versus time graphs. As shown, the phase shift is present, but is not exactly a 90 degree phase shift.

With the voltage probes still connected incorrectly, we change to the right resistance that we used for the calculations and take new data.

Here we take more data with different frequencies. We notice that the shift is different when we changed the frequencies.

We compare our theoretical values to our experimental values for reactance. We explain the large error due to the unknown resistnace in the function generator. Even with the voltage probes in the correct position, there was still large error.

We then find the displacement of the time between two peaks on the voltage and on the current graphs, find the difference and divide by the period.

We take the arctangent of that and find the displacement angle between the two peaks.

As expected, it was not a perfect 90 degree angle and the higher frequency produced a lower angle displacement.

When we make our theoretical calculations, we compare them to the actual experiential ones and find we're not too far off.

Here we calculate the power dissipated by the circuit, but since only the resistor element in the circuit dissipates power, we can't use the standard formula of current times voltage.

We use the derived formula of current squared times resistance and find power through that.

Here we measure the voltage and current with a multimeter.

Here we took the correct graph with LoggerPro and will now use the data to compare to our collected data from the multimeter.

We learn about the resonate frequcney in the LRC circuits where the capacitive reactance and the inductive reactance cancel out and the circuit is a purely resistance circuit.

We derive that frequency to be 1 / (2\pi * inductance * capacitence).

We calculate a frequency and compare it to our measured frequency from the multimeter.

We hooked up the RLC circuit to the function generator as normal, but then adjusted the dial on the function generator until the current reached its peak. 

We compare this experimental value to our theoretical value and find a percent error. Again, we attribute this error to the unknown resistance in the function generator.