# A lab experiment to understand the voltage difference between the resistor indicator and capacitor

### Physical Principles

Capacitors A capacitor has the ability to store charge. However, since the charges must flow through the resistor, R, the charging does not occur instantaneously.

A graph of this function of charge vs. The characteristic decay time is again given by RC. A single-pole, double throw switch is also included. When the switch is in position a, the charge on the capacitor and hence the voltage across the capacitor increases with time.

1. Instead of paying 60 cents one time at one booth, they would now have to pay 20 cents three times at each of the three tollbooths. If current is cut from any one of them, it is cut from all of them.
2. In order for the refrigerator to work in that kitchen, the toaster oven, dishwasher, garbage disposal and overhead light would all have to be on.
3. The flow of charge through the wires of a circuit can be compared to the flow of cars along a tollway system in a very crowded metropolitan area.

After the capacitor is fully charged, the switch is moved to position b, and the charge on the capacitor and hence the voltage across the capacitor will decrease with time. An inductor is a coil of wire that opposes changes in the current. The amount of resistance to change in current depends on a parameter called the inductance, L, which depends on the number of turns and geometry of the coil.

Figure 4a shows an inductor, resistor and voltage source connected in series. The current as a function of time is given by: Capacitors in Series and Parallel Figure 5: Series Using the capacitance meter, measure directly the capacitance of each of the two capacitors in the circuit board. Connect the two capacitors on the circuit board in a parallel arrangement see Figure 5and measure the total capacitance. Connect the two capacitors in a series arrangement see Figure 6and measure the total capacitance.

Calculate the expected capacitances of the two configurations using eqs, 1 and 2.

• They can be connected in series or connected in parallel;
• It is clear from observing the indicator bulbs in the above diagrams that the addition of more resistors causes the indicator bulb to get brighter;
• If adding the tollbooths i;
• Select the best data and fit it to an inverse exponential curve;
• Determine the percentage error between calculated and measured values.

Determine the percentage error between calculated and measured values. Set up the circuit as in Figure 7. Be sure the lab instructor or TA checks the circuit before you turn the power on! Note that the probes to Channel A of the Science Workshop Interface are set to measure voltage which is proportional to charge across the capacitor. Connect the red lead from the red plug on the power supply to one side of the switch.

Connect the bottom end of the capacitor to one end of the resistor, as shown, and connect the other end of the resistor to the middle of the switch. Once your circuit has been checked, turn the voltage source up to about 8 V.

### Capacitance and Inductance

Do not exceed 10 V. Open Data Studio and click Create Experiment. Click on Channel A and select Voltage Sensor from the list. Set the stop time to 5 seconds. Open a Graph display by double clicking on the Graph icon in the left column.

## Two Types of Connections

The graph should look similar to that of Figure 1b. Select the best data and fit it to an inverse exponential curve. Paste a copy of your graph in your e-journal. Record the value of the steady state charged value of V0.

Draw a circuit diagram of the experiment you just ran. Include the voltage source, the switch, the resistor, and the capacitor.

## General Physics Experiment 4

How does the amount to electrons gathered on the negative side of the plate change as time goes on? What does this do to the current? Call over a TA or instructor and explain your conclusion to them. Have your ID card ready to scan to receive credit for your explanation.

The graph should look similar to that of Figure 2b. Select the best data and fit it to a natural exponent. Copy your graph to your e-journal. Record the time constant. Using the circuit diagram from checkpoint 1,describe the flow of electrons when the switch is in position B the capacitor is discharging.

Record your measured time constants and capacitance in Table 1.