Introduction

Goals

In this lab you will observe how a capacitor can be charged and discharged and determine the values of a resistor and capacitor using the oscilloscope.

Equipment check

Please make sure your station has all of the following items. If not, check again, then talk to your lab instructor.

• 1 Oscilloscope
• 1 Signal Generator
• 1 Capacitor/Resistor Plate
• 1 Multimeter
• 2 banana cables
• 1 DC Cable Assembly

Basic Concepts

First, let's understand the plot of a function that looks like this: $$\begin{equation} y = A(1-e^{-t/\tau}) \label{eq:exprise} \end{equation}$$ Here, $t$ is the variable for time, and $y$ represents some value that is changing as a function of time. The constant $\tau$ is called the time constant and its value will determine the how quickly the value of y reached its asymptotic maximum. Here is an interactive plot you can adjust $\tau$ on and see the effects.

As you can see, a small value of $\tau$ means the function quickly reaches a maximum. Large time constants however, mean the function takes a longer time to reach the maximum value. Specifically, $\tau$ is the time required to reach 63% of the max value.

If the max value is 30, what will the function described in equation $\eqref{eq:exprise}$ equal after 2 seconds, if the time constant is 6 seconds?

A capacitor, when connected to a voltage source, will allow charges accumulate on its two sides. This process takes some time which can be determined by considering the capacitance of the capacitor and the resistance of the rest of the circuit. Here is a simple RC circuit. The capacitor will eventually be charged by the voltage source. The time it takes for this to happen is determined by the values of the resistor and the capacitor: $$\begin{equation} \tau = R C \label{eq:taudef} \end{equation}$$ This is the definition of the time constant.

Eventually, the capacitor will reach the same potential difference as the batter (or power supply).

Similarly, you can discharge a capacitor. This means you will let the charges that have accumulated on both sides of the capacitor redistribute. This also takes time (but it takes the same amount of time as charging:)

Discharging is described by the following equation.

Experiment 1: just measure something!

First connect the signal generator directly to the oscilloscope as shown.

Create a 100 Hz square wave on the signal generator and make sure you can see the signal on the oscilloscope.

1. You can press AUTO-SET on the oscilloscope face (upper right) and it will try to pick the best settings.
2. Once you see the square wave, play with both the signal generator and the oscilloscope by changing various parameters on both instruments and observing the changes.
3. For example, try the VOLTS/DIV knob or the SEC/DIV knob on the oscilloscope.
4. Try changing the AMPL(litude) knob on the signal generator.
5. Try different waveforms on the signal generator by pressing the WAVE button.
6. Press the CURSOR button on the oscilloscope and then use the position knobs in the center to move the cursor (lines). Notice the region of the display on the right that will tell you either the $\Delta V$ between the cursors or the $\Delta t$, depending on which variable you are measuring. You will need this function later in the lab so do not proceed until you have figured it out. (It might take 10 or 20 minutes - that's ok!) Explore the equipment!

Experiment 2: Measure τ

Set up your equipment as shown in the drawing below.

1. You'll have to use coax cables to connect to the signal generator and the oscilloscope. Coax cable has a center conductor (pin) and an outer shield allowing for two wires to be packaged as one. Pay attention to the shield/pin indications on the drawing.
2. On the signal generator, you'll want to create a square wave that oscillates at 100Hz. Explore the front panel to figure out how to do this.

Some Tips:

1. On the oscilloscope, there is a button called AUTO SET. If you aren't seeing anything that makes sense on the screen, you can always press this and it will try to figure out the best settings based on what's coming in.
2. You'll want CH1 and CH2 to be set to DC coupling.

After some playing around, you should be able to meausure a value for $\tau$ using the CURSOR function on the oscilloscope. This is the only thing you have to do for the lab, so take your time to figure it out. (isn't that more fun than us telling you exactly how to do it?)

Enter your value for $\tau$ here. (Note the units! milliseconds!)

Then use the multimeter to measure the resistance and the capacitance of the resistor and the capacitor. If you multiply these two values together you should get something close to what your measured for the time constant.