6/2 RC and LRC Circuits

Lab Day: 6/2 RC and LRC Circuits

Purpose: Today we will look at AC,RC and LRC circuits where we will analyze how resistors and capacitors, and inductors when arranged together affect the current and voltage relationships. 

We began class by using a function generator connected to a circuit board across a resistor and a capacitor where we derived equations using the impedence factor. The impedence is a measure of the resistances across an inductor, capacitor and resistor and this is important when looking at a whole circuit. It works well even when one factor is not connected. We calculated the Irms as we double the frequency.

Experiment AC: RC Circuit Analysis (AC)

We have a circuit board showing a connection of a resistor and a capacitor(AC)

We began the experiment setup seen using an alternating current and connected a resistor and a capacitor to the circuit. We connected the current meter to logger pro and the results showed a sinusoidal wave form of current and voltage.

We initially setup the function generator at 10Hz and then we looked at the graph using logger pro for the same experiment with 1000 Hz and found a relationship between frequency and current.

We measured the current and voltage seen in the picture and found that the current graph had many bumps which was due to the sampling rate at high frequencies. After adjusting the sampling rate, we fit the graph and used the values for our calculations of theoretical/experimental values.

Using the new equations derived, we eliminate the inductor in our impedence calculations and found the vrms values and Irms values. We recorded our experimental results in the chart displayed on the whiteboard. 

We then calculated the phase angle when it is at 10 Hz and 1000Hz and found that as frequency increases the phase angle becomes a lot smaller. If we were to calculate the power dissipated in our circuit we would use P=I^2R and only look at the resistor.

RLC Circuits

The experiment was repeated with an RLC circuit by connecting a resistor, inductor, and a capacitor to the circuit. The results in the white board on the right shows the results of experiment using the circuit board and multimeter to compare to theoretical calculations. In fact in an RLC circuit, we find resonance when the capacitive inductance of the inductor is equal to the capacitive reactance of resistor. We get that W=1/sq(LC) which occur only in correlation to maximum power.

Conclusion: We looked at different types of circuits in alternating current where we found experimentally with resistors and capacitors (RC circuit) connected in series that the current and voltage is different by a phase angle. When we looked at RLC circuits which is a whole circuit, we found that there was a special case of resonance where the angular frequency is inversely proportional to the inductor and capacitor.