and Capacitors RC Circuits Abstract: In this lab we performed experiments to observe how the RC time constant affects the charging and discharging of capacitors. We first set up an RC circuit and measured the time it took for a capacitor to charge with varies resistances. We then used the capacitor charging equation to verify that our results were correct. Also, through the experiment we realized the relationship between the speed of charging a capacitor and the amount of resistance in the circuit. As the resistance increase so did the time it took to charge the capacitor. We then repeated the experiment with a discharging capacitance and observed the same relationship. While discharging the capacitor we also examined the relationship between the RC time constant and the resistances used and were able to come up with the capacitors capacitance. In another part of the experiment, we charged a capacitor and then placed it in parallel with another capacitor and observed the charges on each capacitor. After performing the experiment we concluded that charge was in fact conserved. In the last part of the experiment we set up a circuit with an LED and capacitor in parallel. By doing this we were able to calculate the LEDs turn on voltage and compare it to the times we recorded with our stop watches. These experiments also tested our knowledge of basic circuit laws like Kirchoff's voltage and current law, ohm's law, and the relationship between elements in series and parallel. Part 1: Charging a Capacitor In the first part of the experiment we created the RC circuit shown in figure 1 and used it to measure the time it took a capacitor to charge to a certain voltage. The capacitor was 2200 microfarads and the resistor box was set to 10k ohms. The voltage source was then set to 3V and we measured that the maximum voltage the capacitor reached was 2.99V. We then changed the voltage source to 5V and the capacitor charged up to 4.99V. The voltage difference is very slight, so it can be negligible due to the human and machine error. Through this experiment we can conclude that the capacitor can only charge to the voltage of the power supply.
Figure 1 (RC Circuit) Next, we wanted to measure the time it took to charge the capacitor and then use the equation below to calculate the time constant of the circuit.
Equation 1 The power supply was kept at 5V and we measured the time it took the capacitor to get to 3V. We found the time to be 23.1 seconds and then plugged it into equation 1 above. The resulting answer was 3.25V, which is very close to the 3V we were expecting. The difference in voltage could be due to human error in mistiming or the resistance in the wires or equipment we used could have affected the results. Next we wanted to observe how the resistance affected the time needed to charge. In table 1 below you can see the resistance used and the time it took to charge the capacitor.
Resistance 1k ohms 5k ohms 10k ohms 15k ohms Time to Charge 2.0 sec 14.9 sec 23.1 sec 33.3 sec
Table 1 (Charging Capacitor) As the resistance increased, the time need to charge the capacitor increased. Figure 2 below is a graph of the results. The slope of the line created is the inverse of the capacitance. Using the chart we calculated the inverse of the slope to be 2.16e-3 farads. The capacitance written on the capacitor was 2.2e-3 farads. The measured capacitance and the capacitance written on the capacitor are extremely close.
Resistance vs. Time
16 14 12
Resistance (k ohms)
10 8 6 4 2 0 0 10 20 Time (sec) 30 40 Series1
Figure 2 (Charging Capacitor) The slight difference between the two capacitances could be due to human error in measuring the time. The response time for clicking the start and stop button on the stop watch could be the difference between being 100% accurate. Also, the written
capacitance on the capacitor may not be accurate. The capacitor could have leakage, so that could have an affect on the results. The wires and equipment we used might have had some resistance to them, which was not taken into consideration with the calculations. Also, the accuracy of the voltmeter and the power supply could be put into question. Part 2: Discharging a Capacitor In part 2 of this experiment we constructed the circuit in figure 3 below. The capacitor was charged fully and then we timed how long it took to discharge. The fixed resistor was 1k ohms, the power supply was 5V, and the capacitance was 4700 microfarads.
Figure 3 (RC Circuit) The time constant for charging the capacitor was very fast, because it only went through the 1k ohms fixed resistor. However, when discharging we varied the resistance with the decade box. Table 2 below shows the amount of resistance in the circuit and the time it took the capacitor to discharge to 10% of its original charge. As can you see, when the resistance is increased, the time it takes to discharge is increased too. The third column is the time constant for the circuit at the given resistance. We used Equation 2 to find the time constant using the initial voltage, final voltage, and time to discharge.
Resistance 1k ohms 3k ohms 5k ohms 10k ohms 20k ohms Time to Discharge 11.1 sec 35.1 sec 57.4 sec 117.3 sec 238.1 sec Time Constant 4.8 15.2 24.9 50.9 103.4
Table 2 (Discharging Capacitor)
Equation 2 We then graphed the RC time constant as a function of the resistance in figure 4 below. By using the graph we can determine the capacitors capacitance. Using the slope of the graph we calculated the capacitance to be 5.2e-3 farads. The capacitance written on the capacitor was 4.7e-3.
There are many reasons that there is a difference between the measured capacitance value and the written capacitance value. The same experimental errors in the previous part of the experiment still hold true here. Leakage in the capacitor could make the actual capacitance different then what is written on it. The resistance in the wires and equipment could have made the calculations inaccurate. Also, human error in timing the capacitors discharge.
RC vs. Resistance
120
100
RC Time Constant
80
60
Series1
40
20
0 0 20 40 60 Resistance 80 100 120
Figure 4 (RC vs. Resistance) Part 3: Stored Charge and Parallel Capacitors In this part of the lab we observed how the charge of a capacitor would be affected by another capacitor in parallel. We constructed the circuit shown in figure 5. The resistor was 1k ohm, the first capacitor (C1) was 2200 microfarads and the second capacitor (C2) was 1000 microfarads.
Figure 5 (Capacitors in parallel) In order to perform this experiment we disconnected the C2 and charged C1 to 5V. We then used the equation Q=VxC to find the total charge in C1. The total charge came out to be 1.09e-2C. Then we connected C2 in parallel with C1 and found the voltage to be 2.44V across each. We then plugged in the voltage and capacitance for each of them into
the equation Q=VxC. The charge in C1 was 7.57e-3 and the charge in C2 was 3.44e-3C. These numbers show that the capacitor with the higher capacitance holds more charge. By adding the two charges together we got 1.10e-2C which is very close to the original 1.09e-2C. This shows that charge is conserved. Part 4: Analog Timer In part 4 of this experiment we placed an LED in parallel with a capacitor like in figure 5 below to find the time it takes to turn on the LED.
Figure5 (Analog Timer) We turned on the power supply and opened the switch and timed how long it took to turn on the LED. We tried three capacitors and recorded the time it took for the LED to turn on at each capacitance. The results are in table 3 below. As you can see, the maximum voltage the capacitor reached each time was 1.65V. This leads us to believe that the turn on voltage for the LED is 1.65V since the LED is in parallel with the capacitor. We also calculated the time it would take the LED to turn on using the RC charging equation and found that it was accurate each time.
Capacitance 1000 microF 2200 microF 4700 microF Time (For LED to light) 4.3 sec 8.9 sec 15.7 sec Calculate Time 4.0 sec 8.8 sec 18.8 sec Maximum Voltage 1.65 V 1.65 V 1.65 V
Table 3 (Analog Timer) We used the data in the charge to graph time as a function of capacitance as seen in figure 6. The line has a fairly defined slope, proving that the RC constant is in effect.
Analog Timer
20
Time (sec)
15 10 5 0 0 2000 4000 6000 Capacitance (microfarads) Series1
Figure 6 (Analog Timer)
Analog Timer Our analog led timer is able to provide various timings according to the capacitor used in the circuit. When the desired time is reached the LED will light, letting you know that the time has been achieved. Various capacitors can be used in this circuit, making the timing choices almost unrestricted.
Figure 5 (Analog Timer) We used the circuit diagram in figure 5 in our timer model. The device works by having an LED in parallel with a capacitor. Once the capacitor reaches the LED's turn on voltage, the LED will light. We are able to determine the LED's turn on voltage using the RC charging equation. Once we knew the turn on voltage we were able to determine how long it would take the capacitor to reach that voltage using the capacitor charging equation. We repeatedly performed tests with various capacitances and compared them to our calculated times. The chart in table 3 below shows the results we got from the experiment. Each time the times were within 16 percent or better of the expected time.
Capacitance 1000 microF 2200 microF 4700 microF Time (For LED to light) 4.3 sec 8.9 sec 15.7 sec Calculate Time 4.0 sec 8.8 sec 18.8 sec
Table 4 (Predicted vs. Measured Led Turn on Time)