Part B - Alternating Current and RC circuits:

If a sine-wave AC voltage is applied to a series RC circuit, Ohm's law becomes V = IZ, where Z is the series impedance produced by the resistance R in series with the capacitive reactance of the capacitor, $X_{c} = 1/2 \pi fC$. The total impedance Z is given by

$$Z = \sqrt{(R^{2} + X_{c}^{2})}.$$

The impedance looks like the vector sum of two impedances, the hypotenuse of a right triangle whose base is $R$ and whose altitude is $X_c$. What is the significance of the angle between the hypotenuse and the base? Yes! It is the phase angle between the current and the voltage. Calculate the frequency at which this angle should be $45^0$, set the function generator to that frequency, and measure the phase difference. Then, measure the voltage amplitudes of the source, the resistor, and capacitor, and check to see if these add like vectors. Recall that Kirchhoff's voltage loop rule says that the voltages around a loop add like scalars.