Lab
ENGTECH 1EL3 | 1 Lab 7: Transient in RC Circuits IMPORTANT INSTRUCTIONS ABOUT THIS LAB 1. THIS LAB WILL NOT BE DONE INDIVIDUALLY. THE LAB WORK MUST BE DONE IN GROUPS OF 2 STUDENTS. 2. IGNORING THE WARNINGS (HIGHLIGHTED IN RED) IN THIS LAB MANUAL MIGHT RESULT IN INJURIES. PLEASE READ THEM CAREFULY AND IMPLEMENT ALL INSTRUCTIONS. 3. Objectives • Study the steady-state behavior of a capacitor • Determine the time constant of an R-C network. • Obtain the charging voltage of two capacitors in parallel. • Obtain the charging voltage of two capacitors in series. • Obtain the charging current. 4. Introduction • A capacitor at steady-state behaves as an open circuit. • When a dc source is applied to an RC circuit, the capacitor cannot change its voltage discontinuously. The capacitor voltage will start from zero and as the current begins to flow, the capacitor acquires a charge and its voltage increases. The rate of this charge is determined by the time constant ? and is equal to the product of ??. In one time constant, a capacitor will charge up to 63.2% of its final voltage and in five-time constants it is charged up to 99.3% of final voltage. • The charging equations for the voltage and the current can be written as ?? = ? (1 − ? − ? ?) ?? = ? ? ?− ? ? ? = ?? 5. Equipment • Power Supply • Multimeter • Resistors • Capacitors • Breadboard ENGTECH 1EL3 | 2 6. Procedure Part 1: DC Steady-state behavior of an RC circuit 1. Set the voltage of the power adaptor to 5V. WARNING THROUGH THE WHOLE LAB, YOU MUST SET THE ADAPTOR TO PRODUCE 5V. SOME COMPONENTS THAT WILL BE USED IN THIS LAB HAVE A MAXIMUM VOLTAGE OF 6.3 V. INCORRECT SETTING OF THE POWER ADAPTOR CAN LEAD TO EQUIPMENT DAMAGE AND/OR SERIOUS INJURY 2. Construct the circuit shown in Figure 1. 3. Measure ?1, ?2 and ?1 and record your measurements along with their theoretical values. 4. Calculate the theoretical steady-state values for all voltages (?1, ?2, and ??) and currents (?1, ?2, and ??) of the circuit shown in Figure 1. 5. Energize the circuit and measure the source volage ? and the voltages ?1, ?2, and ??. Make sure to take the readings when the circuit reaches steady-state. This should happen very quicky due to the small time constant of the circuit. 6. Measure the currents ?1, ?2, and ??. Remember to disconnect the power every time you modify the circuit to measure the current. Figure 1. Figure 1. ENGTECH 1EL3 | 3 Part 2: Transient behavior of an RC circuit 7. Construct the circuit shown in Figure 2. a. The effect of opening/closing the switch S1 will be emulated by disconnecting/connecting the barrel jack connector of the power adaptor from/to the 2-terminal connector (see Figure 3). b. The effect of opening/closing the switch S2 will be emulated by disconnecting /connecting a jumper wire between Nodes a and b (see Figure 3). WARNING DO NOT USE THE 100 ?F ELECTROLYTIC CAPACITORS IN YOUR KIT AND USE THE 100 ?F CERAMIC CAPACITORS THAT WILL BE PROVIDED TO YOU BY THE LAB INSTRUCTOR. INCORRECT USE OF THE ELECTROLYTIC CAPACITORS IN YOUR LAB KIT MAY CAUSE A SERIOUS INJURY + _ vC + _ vR a b Figure 2. disconnecting/connecting the barrel jack connector will be used to simulate S1 opening/closing disconnecting/connecting the jumper wire will be used to simulate S2 opening/closing Figure 3. ENGTECH 1EL3 | 4 8. Measure ?1, ?2, ?3 and ?1 and record your measurements along with their theoretical values. 9. Calculate the theoretical time constant of the charging circuit (S1 is closed and S2 is opened). 10. Connect the voltmeter to measure the capacitor voltage ?? . 11. To make sure that the capacitor is initially discharged, close S2 by connecting the jumper wire between Nodes a and b. After a couple of seconds, open S2 by removing the jumper wire. 12. Measure the time constant of the charging circuit by doing the following a. Confirm the capacitor voltage is initially zero. If this is not the case, discharge the capacitor by performing step 11. b. Calculate 63.2% of the steady-state capacitor voltage using 0.632 × ? c. Prepare a stopwatch on your phone or a watch to measure the time elapsed d. Energize the circuit by closing S1 (connecting the barrel jack to the 2-terminal connector) and start your stopwatch e. Record the time at which the multimeter reads 0.632 × ?. This value is the time constant of the charging circuit. 13. Wait until the circuit reaches steady-state (the capacitor voltage is almost constant and has a value that is very close to the supply voltage) 14. Open S1 by disconnecting the barrel jack of the power adaptor. 15. Measure the voltage across the capacitor. Is there a reading? Why? 16. Discharge the capacitor by doing the following a. Close S2 by connecting a jumper wire between Nodes a and b. b. Once the capacitor is fully discharged, i.e. the voltage read by the multimeter is approximately 0 V, open S2 by removing the jumper wire. 17. Is the discharging time of the capacitor faster or slower than the charging time? Explain why. 18. Using a watch, record (to the best of your ability) the voltage across the capacitor at time intervals: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100 sec after closing S1 (connecting the supply to the circuit). Again, be sure to discharge the capacitor between each run. 19. Calculate the charging current for each measurement in step 18 using ?? = ?? ? = ? − ?? ? 20. Plot the curves of ?? and ?? versus time and include it in your report. 21. Modify the circuit in Figure 2 to have two 100 ?? capacitors in parallel and measure the time constant of the charging circuit as described in Step 12. 22. Modify the circuit in Figure 2 to have two 100 ?? capacitors in series and measure the time constant of the charging circuit as described in Step 12. CHECKPOINT: SHOW YOUR RESULT TO THE LAB INSTRUCTOR ENGTECH 1EL3 | 5 Part 3: Multisim Simulations Please complete this part at home. 23. Construct the network shown in Figure 4. a. you will be using a new component, a single-pole single-throw (SPST) switch, which can be found in the Switches library. b. Set the ROFF for S1 to 100G c. Set the ROFF for S2 to 100M d. add a Voltage and Current measurement at the top terminal of the capacitor. Figure 4 24. Click on the Run Simulation button and the Split button. ENGTECH 1EL3 | 6 25. Your screen should appear like the one below. Try to pan the circuit schematic till the instantaneous value of ?? and ?? can be seen while the screen is splitted 26. Click or double click on the circuit schematic and notice that the scope/grapher is grayed out and the menu at the right of the screen is showing the Document tab. 27. Click or double click on the scope/grapher and notice that the circuit schematic is grayed out and the menu at the right of the screen is showing the Item tab. 28. Scroll down the item tab and set the Time/Div to 5 s/div, the Minimum/Maximum Voltage to -5/5 V and the Minimum/Maximum Current to -50e-6/50e-6. Charging phase 29. In the circuit schematic, close S1 by clicking on the switch. This will connect the battery to the RC circuit. 30. Observe the time variations in the scope. 31. Wait until the capacitor voltage is greater than or equal to 4.97 V (steady-state) and then click on the pause simulation button . 32. In the item tab, set the minimum time to 0 s. This will allow the display of the full waveform of the capacitor voltage. 33. Hover your mouse on the voltage waveform and notice that a data curser appears and show the time and voltage value for the point corresponding to your mouse position. Figure 5. ENGTECH 1EL3 | 7 34. From the scope plot, measure the time constant, ?, of the circuit (the time it takes from the instant of switching, see the figure 5, till the capacitor voltage reaches 63.2% of its steady-state value). 35. Measure the capacitor voltage after 5?. 36. Measure the maximum capacitor current at the instant of switching. 37. Measure the capacitor current after 5?. 38. Include your graph in your lab report. Discharging phase 39. Resume the circuit simulation by pressing the run button . 40. Open S1 by clicking on the switch S1. 41. Close S2 by clicking on the switch S2. 42. Stop the simulation. 43. Scroll back in time by clicking on the scope and dragging your mouse to the left. Try to display the transient during the discharging of the circuit. 44. In the item tab, a. set the Minimum/Maximum Current to -50m/50m. b. Adjust the time Minimum/Maximum time difference to be relatively short (around 0.2 s) c. The graph should look similar to the one below 45. Include your graph in your lab report. 7. Analysis Questions 1. Perform DC steady-state analysis for the circuit in Figure 1 and calculate all the circuit voltages and currents. 2. Write equations for the capacitor voltage and current for the circuit in Figure 2 when S2 is opened and S1 is closed at t = 0. Assume zero initial voltage. 3. Answer all questions within the procedure section. 8. Lab Submission 1. Please submit a report for this lab. The report must follow the format described in “1El3 Lab Report Format” document on Avenue to Learn under the Contents>>Labs. ENGTECH 1EL3 | 8 L8 Record Sheet Part 1: DC Steady-State Step 3 R1 R2 C1 Theoretical Measured Steps 4, 5, and 6 ? ?1 ?2 ?? ?1 ?2 ?? Calculated Measured Part 2: Transient Analysis Step 8 R1 R2 R3 C1 Theoretical Measured Steps 9 and 12 ? Calculated Measured Step 15 Capacitor Voltage when S1 and S2 are open Calculated