AC Signals

The analyzation of AC circuit is a very big and important part of electrical engineering. One way to solve for unknowns in AC circuit is using differential equations, however this method could be very time consuming and open to making errors. As a result using phasor analysis for AC circuit has become very popular because of its simplicity compare to differential equation. At first this method might seem a little confusing to beginners but after a while it will get easier and eventually would be preferred over other methods.
In this lab while trying to learn about different aspects of a simple RC circuit, we tried to solve problems using phasors.
First we connected our function generator(FG) to channel 1 of our oscilloscope(O-Scope) and set the FG for a 10V peak to peak sinusoid at 1kHz. With screen readings of 2V per division the Vrms became 3.354 V. Then we connected the FG to DMM to measure VAC and Vrms became 3.3V. The 3.3 V shown by the meter is off because these meters are not designed to operate in high frequencies.
If we were to connect a 100 nF capacitor to this circuit, its impedance would be -1592jΩ.

After the calculations we constructed the above circuit.
Vcap, peak_peak=8.2V
Vcap,rms calculated = 2.9 V
Vcap,rms measured = 2.78 V
In this case values are close since we are not using very high voltages.
tx is the time difference between the two waveforms.
tx=83.78 μs
Φ is the phase angle between the two wave form and it can be obtained using Φ=2πft=0.526 rad or 30.16 degrees.
The following is a graph of the two wave form.
tx had to be small enough to place the angle between 0 and 2π. so we set 2πft equal to 2π and 0 which gave us time scale between 0 and 1 ms.

 For the next part of the experiment we increased the FG frequency to 10kHz. This brought down the capacitor impedance by a factor of 10 to -152.9kΩ, which in turn changed the Vcap, peak_peak to 1.68V.

Vcap,rms calculated = 0.6 V

Vcap,rms measured = 0.429 V

this shows as we increase the frequency the DMM proves to be less efficient.

tx=22.16 μs

Φ=1.39 rad or 79.8 degrees

This graph clearly shows that the offset has increased.

Next we brought the frequency back to 1kHz but increased the resistor box to 10kΩ.

Vcap, peak_peak=1.69V

Vcap,rms calculated = 0.597 V

Vcap,rms measured = 0.6V

since we are back at the low frequency DMM measures accurately.

tx=216.22 μs

Φ=1.36 rad or 77.84 degrees

Next we toggled the value of the resistor box to get exactly 4V peak to peak.

For that to happen the value was 4kΩ.

Vcap, peak_peak=4V

Vcap,rms calculated = 1.414 V

Vcap,rms measured = 1.4 V

tx=183.78 μs 

Φ=1.155 rad or 66.16 degrees

As we went from lower to higher frequencies, the capacitor voltage amplitude decreased. So this current circuit would be more efficient as a low-pass filter since for high frequencies it does not create big enough voltages. As we increase the frequency the phase angle between the waveforms increases.