What is the function of universal interface pasco 850

Safety and Equipment No special safety precautions are necessary for this lab. Computer with PASCO 850 Universal Interface and PASCO Capstone PASCO Voltage Sensor (Round DIN to two Banana plugs) 2 Power Supply cables (Banana plugs with slip-on Alligator clip on one end) 2 double alligator wires.

Introduction When a DC voltage source is connected across an uncharged capacitor, the capacitor starts charging quickly. The only thing opposing the flow of current is any resistance in the circuit. But, as the capacitor fills, the potential of each plate gets closer to the potential of the corresponding terminal of the power supply. The drop in potential difference between a terminal of the power supply and a plate of the capacitor reduces the flow of current. This makes the rate of charging decrease as time passes. At first, the capacitor is easy to charge because there is very little charge on the plates and potential difference between a plate and a terminal is large. But as the charge accumulates on the plates, it becomes more difficult for the power supply to move additional charges onto the plates because the plates already have a charge of the same sign as the terminals on them. As a result, the capacitor charges exponentially, quickly at the beginning and more slowly as the capacitor becomes fully charged. The charge on the capacitor at any time is given by:

The voltage across the capacitor is proportional to the amount of charge on the capacitor:

The voltage across the capacitor at any time is given by:

Where Vmax is the maximum voltage of the capacitor, and is the capacitive time constant ( = RC, where R is resistance and C is capacitance). The time constant describes the rate of the charge of the capacitor. The greater the time constant the longer it takes to charge the capacitor and vice versa. NOTE: Taking the extreme limits, notice that when t = 0, V (0) = 0 which means there is not any charge on the plates initially. Also notice that when t goes to infinity, V approaches Vmax. For any finite t, the voltage is less than Vmax, which means it takes an infinite amount of time to completely charge the capacitor.

Objective: Experimentally determine the time constant of the R-C circuit. Investigate how a resistance affects the rate of charging of a capacitor

Figure 1. (a) The PASCO Voltage Sensor, which acts as a voltmeter for our purposes.

(b) The 1.0 F capacitor. The black stripes on the right side indicate the negative terminal.

Do not hook up the capacitor backwards!

Part #1. Data Recording

(a) (b) Figure 2. Schematic diagram of RC circuit for (a) charging and (b) discharging of the capacitor

1. Very carefully insert Voltage Sensor into analog input A. 2. Discharge the capacitor by placing a metal object directly across it. 3. Use a double alligator wire to connect the 1.0 4. Construct the circuit shown in Figure 2(a) with Voltage Sensor connected across the capacitor but wait

on connecting of Power Supply to the resistor (do not connect an alligator clip yet). 5. Experiment 6. Simultaneously connect the loose ends ) and start the Capstone recording. 7. Stop recording when the voltage across the capacitor reaches 4.2V. 6. Highlight and Copy values of both, time and voltage, and transfer them to Excel spreadsheet. 7. Pull cables from the terminals of the Power Supply but wait to connect them together to discharge. 8. Connect the loose ends with a double alligator wire as shown in Figure 2(b) and instantly start recording. 9. Stop recording when the voltage across the capacitor gets below 0.5V. 10. Highlight and Copy values of both, time and voltage, and transfer them to Excel spreadsheet. 11. 12. In Capstone, move to the next page ( ). Repeat 2-10. 13. 14. In Capstone, move to the next page (10 ). Repeat 2-10

Part #2. Analyzing the Data

1. Plot data collected during charge of the capacitor as three series of V vs. t on the same chart. 2. Compare three graphed series and describe how the difference in the value of the resistance affects the

rate of charge of the capacitor. Include this statement in the abstract. 3. Plot data collected during discharge of the capacitor as three individual V vs. t charts. 4. Fit each plot into exponential function and display the equation of the trend line on the graph. 5. Replace Y with V and X with t in the equation. 6.

HINT: The voltage across the capacitor during the discharge varies by: 7. Compare three calculated time constant and describe how the difference in the value of the resistance

affected the rate of discharge of the capacitor. Include this statement in the abstract.

RC Circuit Trendline equation Time constant

RC circuit with 10

Table 1. Experimental results of the discharging capacitor where time constant was calculated from a trendline equation