Resistors, Capacitors, and Inductors in an AC Circuit(5/28/2015)

Day 25, Page 11

Alternating Currents and Voltages

For this experiment, we put together an AC circuit as shown above, which consists of a resistor and function generator (set at 2V and 0.01A). This was all connected to Logger Pro, in order to gather readings on current and voltage flowing through the circuit. We needed this data in order to calculate the V(rms), I(rms), and percent error. The second set of data we are going to use to compare with the first set is the result of readings taken from our circuit using a digital multimeter.

Graphs of Potential V vs Time, Current vs Time, and Current vs Potential Voltage.

After we took readings, we calculated what our expected V(rms) and I(rms) would be based on the graphs shown above. We then tested for our actual V(rms) and I(rms) using a digital multimeter. These values can be seen below, along with our percent errors that we were able to calculate now that we received two sets of data. We received acceptable error percentages, so the experiment went smoothly.

Capacitor Circuit

Depicted above is our calculation and representation of how when a sinusoidal voltage source is connected across a capacitor, then the charge on the capacitor and the current to the capacitor also vary sinusoidally with time.  The voltage and charge are related by v = q/C, so the charge and voltage are in phase.  However, the charge lags the current by 90^o, so it is found that the voltage lags the current by 90^o.

The calculation shown below refers to an example problem, which states that a 0.02 mF capacitor is connected to a 50Vrms AC voltage source which oscillates at 10 kHz. We are asked what the Irms is to the capacitor.

Capacitors in an AC Circuit

As with the first experiment we have a circuit shown above, but instead of a resistor being used we have a capacitor hooked into the circuit along with the function generator. The function generator was set to 2V and 0.16A(rms), so twice as much voltage was used this time and a significantly increased I(rms).

After getting the data shown above, we were able to calculate the expected and actual voltage and current in the system exactly as we did in the first experiment. We used our data and equations for V(rms) and I(rms) to calculate our theoreticals, and then tested the actual voltage and current in the circuit using a multimeter. Unfortunately, this time it seems we ended up with a very high percent error, but this seemed common among the class. Now that we delved into phase shifts, we also calculated phase values for our circuit.

Inductors in Alternating Circuits

For this final lab we used the same circuit as before, except instead of a capacitor or resistor, we now tested out this same system using an inductor. We again ran a current through using a function generator, collected data (shown above), calculated expected values for I(rms) and V(rms) using our data, and then took actual readings using a multimeter. Our values (seen below) are slightly better in regards to the percent error, but the error is still rather high.

Summary:

In summation, we created three circuits which consisted of a function generator and one of three other components, which were a resistor, capacitor, and inductor. What we saw was that the V(rms) value was the highest in the resistor circuit, and lowest in the inductor circuit. The I(rms) was opposite, as it was lowest in the resistor circuit, and highest in the inductor circuit.