Capacitors in Circuits EQUIPMENT NEEDED: – – – – AC/DC Electronics Lab Board: Capacitors, Resistors, Wire Leads Battery Digital Multimeter Stopwatch or timer with 0.1 sec resolution. Purpose: to determine how capacitors behave in R-C circuits. The manner in which capacitors combine will also be studied. Background: Read the relevant chapter of your textbook (DC circuits). The diagrams for a charging and discharging capacitor are shown below Experimental procedure: a. measurements of the circuit components: Your circuit board contains a battery, 2 resistors and 2 capacitors. 1. Use the color code picture below to identify the resistors: 2. Record in Table 1 the resistance of the resistors by the color code. Due to the likelihood of color confusion, it is wise to also measure the resistance using a multimeter. This time, use the multimeter across each resistor, with the dial initially on the resistor scale (MΩ) and record in Table 1. Do not forget to convert from MΩ to kΩ (multiply by 1000). 3. Now take a look at the two capacitors placed on the circuit board. Read the value written on them and record in Table 2. 4. From the data of Tables 1 and 2 calculate the time constants for all four possible combinations of one resistor with one cpacitor and write them in Table 3. Despite the fact that resistances and capacitances are given in kΩ and μF, when you calculate the time constant τ you have to convert them to Ω and F. 5. Measure the voltage at the battery using the digital multimeter and record it in tTable 4. 6. The time constant τ=RC is the amount of time it takes for a discharged capacitor to store 63% of the maximum voltage (the battery’s emf) or for a charged capacitor to reach 37% of the maximum voltage. Based on this fact, calculate at what voltage reading will you reach one time constant both charging and discharging. Write your values in Table 4. b. Time measurements Figure 1 1. Connect the circuit shown in Figure 1, using one battery, the switch, a resistor and a capacitor. 2. Connect the Digital Multimeter so the black “ground” lead is on the side of the capacitor that connects to the negative terminal of the battery and set it so that it reads up to a maximum of 1.5 V DC (max voltage at the battery). 3. Start with no voltage on the capacitor and the switch off. If there is remaining voltage on the capacitor, use a piece of wire to touch the ends of the wire to points B and C as shown in Figure 1 to discharge the capacitor. 4. Now close the switch by pushing and holding the button down. Observe the voltage readings on the Multimeter: the voltage across the capacitor grows. 5. If you now open the switch by releasing the button, the capacitor should remain at its present voltage with a very slow drop over time. This indicates that the charge you placed on the capacitor has no way to move back to neutralize the excess charges on the two plates. 6. Connect a wire between points A and C in the circuit, allowing the charge to drain back through the resistor. Observe the voltage readings on the Multimeter as the capacitor discharges. 7. Now repeat steps 3-5, this time recording the time taken to move from 0.0 volts to the voltage after one time constant when charging, tC (calculated previously at point a.6) while charging, and the time taken to move from the battery voltage to the voltage after one time constant when discharging, tD (also calculated at point a.6). 8. Record your times along with the resistance of resistor 1 and capacitance of capacitor 1 values in Table 5 and the averages in Table 6. 9. Replace the capacitor 1 with capacitor 2 (you got two different capacitors on the board), keep the same resistor 1 and Repeat step 7, recording the charging and discharging times in Table 5 and the averages in Table 6. 10. Return to the capacitor 1, but change the resistor, now use resistor 2 in the circuit. Repeat step 7, recording your data in Table 5 and the averages in Table 6. 11. Take now the larger of your resistors, but use capacitor 1 in series with capacitor 2. Calculate the equivalent capacitance (show your calculation) 12. Repeat step 7, recording your results in Table 7 and the averages in Table 8. 13. Take now the smaller of your resistors, but use capacitor 1 in parallel with capacitor 2. Calculate the equivalent capacitance (show your calculation) 14. Repeat step 7, recording your results in Table 7 and the averages in Table 8. Note: except the student closing the switch, all students in each group should measure the charging and discharging times, record them and calculate the averages and standard deviations. Lab report Table 1: resistors Resistor Color code Resistance by color code (kN) Red-Violet-Yellow-golek 270 KS2 15% Brown-red-Yellow-gold 120kr I 5% Resistance using multimeter (kS2) 270 123.2 Resistor 1 Resistor 2 Table 2: capacitors Capacitance (uF) Capacitor Capacitor 1 Capacitor 2 330 100 The time constant t is defined by the product between resistance and capacitor and it is measured in seconds. Use t =RC and your knowledge of units for both resistor and capacitor, to prove that t is measured in seconds. HINT: show how units cancels out and what is left is seconds. Show your work below: T=RC (s) Table 3: time constants Resistor R (k22) Resistor 1= 270 Resistor 2= 120 Resistor 1= 270 Resistor 2= 120 Capacitor (UF) Capacitor 1= 330 Capacitor 1= 330 Capacitor 2= 100 Capacitor 2 = 100 89. 1 39.6 27 12 V Table 4: voltages Measured emf of the battery Voltage after one time constant when charging Voltage after one time constant when discharging €= 1375 V= 866-25 V= 508.75 V 0.63 0.37 V Tcharge (s) trial 2 Tcharge (s) trial 3 T discarge (s) trial 2 34.2 34.2 2 15.5 Table 5: recorded times Tcharge (s) trial 1 Student 1 49.8 Student 2 50. 4 Student 3 49.5 Student 4 50.4 Student 5 49.9 Tdiscarge (s) trial 1 48,9 48,4 49.7 49.6 48,9 35.5 33,2 Tdiscarge (s) trial 3 14.2 14.8 14.2 1407 H2 15.9 3 4.7 35.3 33.6 33.5 33.2 Z منار جرم average Standard deviation Table 6: times for one resistor and one capacitor. Trial Resistance (kN) Capacitance (UF) 1 tc (s) to (s) TERC 2 3 Calculate the equivalent capacitance for the two capacitors in series, using the formula 1 1 + Ceq C1 Show your calculation: C2 Calculate the equivalent capacitance for the two capacitors in parallel, using the formula Ceg=C1+C2 Show your calculation: Table 7: recorded times Tcharge (s) parallel Student 1 Student 2 Tcharge (s) series 12.76 12.08 12.27 12.86 12.67 Tdiscarge (s) series 11.07 17,99 11,63 1. 78 11.67 Tdiscarge (S) parallel 62.28 63.18 62.32 62.48 62,23 Gluc8 64.34 64.39 64.6 64.59 Student 3 Student 4 Student 5 average Standard deviation T(s) tc (8) Table 8: times for one resistor and two capacitors Type of Circuit R (0) Cea (uF) Series 120 100 Parallel 120 430 to (s) c. Discussion: 1. How would you describe the manner in which the voltage across the capacitor grows? Sketch a graph showing the manner in which the voltage rises over time. 2. How would you describe the manner in which the voltage across the capacitor falls? Sketch a graph showing the manner in which the voltage falls over time. 3. Is the charging time of two capacitors in series larger or smaller than the charging time of each of the two capacitors? LARGER SMALLER. Why? 4. Is the charging time of two capacitors in parallel larger or smaller than the charging time of each of the two capacitors? LARGER SMALLER. Why? 5. What is the effect on charging and discharging times if the resistance of the circuit is decreased? What mathematical relationship exists between your times and the resistance?
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