R-C and L-R-C Circuits

This is the graph of the voltages and current in an ac circuit containing a resistor and a capacitor as functions of time. 

Here is our table of values for the capacitive reactance as well as the impedence of a circuit with a resistor and a capacitor. By raising the frequency, we effectively increase the impedence, allowing for a greater potential in the circuit.  

The resonating frequency of an alternating current is given in the top left corner. At three thousand hertz, the rms value for current in this circuit is 2.06 A. To find the power dissipated, we can ignore the inductor and the capacitor, and treat the circuit as if there is only a resistor present. In this circuit the power dissipated is 42.6 W.

In this image we can see that in this ac-circuit, the voltage leads the current by 90 degrees.

Here we have a voltage generator, resistor, ammeter, capacitor, and inductor all connected in series. On the generator, we change the frequency in order to find when it has its maximum current. 

We predicted that the maximum current would occur at 90.6 hertz, when in fact maximum current occurred at 112 hertz. Our experimental error was 19.1%.

Conclusion: The current is maximum in an AC-Circuit when the capacitive and inductive impedences are equal. The voltage across the inductor leads the current by 90 degrees, while the voltage across the capacitor lags the current by 90 degrees. The voltage across the resistor is in phase with the current.

RL-Circuits

Provided the resistivity of an 18 gauge copper wire, the number of turns in an coil consisting of the 18 guage wire, and the length of one side of the coil, we are able to find the resistance of the wire. Then dividing our calculated inductance by this resistance, we were able to find the time constant of this circuit, theoretically

With the switch open, we can find the time constant just by treating the circuit as if all that were present were the inductor and the 120 ohm resistor. 

In the top right corner, we find the time constant for this circuit given the values of the inductor and the resistance. Then we find the the current at 170 microseconds, which turns out to be 0.16 amps. Then we used kirchhoffs laws to find the voltage drop across various circuit elements. As you can see, as time goes to infinity the current reaches EMF/R, but it never quite reaches it because e^-(tR/L) never reaches zero. The current reaches its maximum level asymptotically. The amount of energy in the inductor is represented by one half the product of the inductor and the square of the current.