VI.  RC CIRCUITS

Equipment List:
        Dual trace scope
        HP function generator
        Bread Board
        Assorted resistors and capacitors
        1 BNC-BNC        
        1 BNC-Banana
        1 BNC T-connector
        1 Black Banana-banana
        Scope probe
        Alligators

Theory: When a voltage is applied across a capacitor, the capacitor does not become fully charged immediately; when the voltage is first applied, the current that is charging the capacitor is large, but as the capacitor becomes more and more charged, the current decreases exponentially in time eventually coming to a zero value.

    From Ohm's law, we know the voltage across a resistor increases as the current through the resistor increases; things are different for a capacitor. As the current "through" a charging capacitor decreases, the voltage across the capacitor increases. To see this, refer to the diagram below:

From Kirchoff's Law, the sum of the voltage across the resistor  and the capacitor (VR + VC) is equal to the voltage of the source (the circuit forms one Kirchoff loop. This is true at any instant of time whether the source voltage is AC or DC). As already stated, VR is large when the current through the circuit is large; this means VC must be small since the sum of VR and VC is a constant, Vsource. As the capacitor charges up, the voltage across it will become large (VC = Q/C). The current into the capacitor will decrease because of the Coulomb repulsion a charged capacitor plate has to the introduction of still more charge on itself. Since this is a series circuit, the current through the capacitor will be the same as that through the resistor (IR = IC). When the current gets smaller, VR gets smaller, but its still always true that: Vsource = VR + VC. You should examine the above argument until you appreciate the internal consistency of it.
    
Introduction:
In this lab you will examine the effects of two different AC signals on a RC series circuit, a sinusoidal and a square signal. The discussion above applies to both cases of input signal forms.
Procedure:
I. Construct the circuit as shown below in the pictorial and schematic diagrams.

I. The series RC circuit driven by a square signal: The square function can be thought of as an "on-off" switch; it has two and only two values. The result is that the capacitor is charging and then discharging at a frequency related to the frequency of the square signal. The charging and discharging occur exponentially and the voltage across the capacitor will have an exponential curve throughout this process.
    Measure the voltage across the capacitor and observe this curve. Start at a period equal to about ten times RC. Increase the frequency of the signal and measure VC. Explain what happens and why to the voltage across the capacitor as the frequency increase. If you were to pretend the capacitor was a resistor, would the capacitor act like a large resistor or a small resistor as the frequency increased (hint: think about what happens to the current in the circuit)?

    Graph VC versus frequency. Graph the points while you take the data.

    Note: Since your scope only measures the potential of a point in a circuit with respect to ground, you must make sure the other side of you capacitor is grounded. The scope probe should be placed between the capacitor and the resistor; if the other side of the capacitor is grounded, the scope will measure VC.

II. The RC series circuit driven by a sinusoidal signal:
Change the driving signal on the function generator from square to sinusoid. Set the frequency back to the original 10RC. Increase the frequency and measure VC as a function of the frequency. Explain what you observe.