Answer the "CONCLUSION" part only. Explain your answer preferably in paragraphs format.

II. Experiment No. 6 RC Time Constant OBJECTIVES I ixp'ain the charging characteristics of a capacitor with ac voltage. I ixp'ain the RC time constant and what its value means in terms of circuit characteristics. ' Describe how a capacitor charges and discharges through a resistor as a function of time. ' Explain how an RC time constant may be measured experimentally. THEORY When an RC circuit is connected to a dc voltage source, the charge must flow into the capacitor before the voltage across the capacitor can change. As the voltage across the capacitor becomes closer to that of the source, the flow of charge becomes slower and slower. The capacitor voltage approaches the supply voltage as an asymptote, coming closer but never getting there. When the capacitor starts with no voltage across it, V : O at t = 0, the subsequent changing voltage is given by the equation V==Vo(1-e%) t eq. 6.1 V==Vo(1-e7) where T==RC is the time constant of the circuit V0 is the voltage of the source After a time of one time constant, t==T==RC, the voltage is RC V = V0 (1 e) V = V,,(1 e-l) V = V0(0.63) V __::0_53 eq. 6.2 V0 That is, the voltage across the capacitor is 0.63 (or 63%) of its maximum value. For a dc voltage source, the capacitor voltage further increases to V0 and maintains this voltage unless discharged. Ubhage,v W} v = v.11 r1) - 0.53m, t=RC meJ Figure 6.1 III. IV. However, for an ac voltage source, the capacitor voltage increases and decreases as the voltage of the applied signal alternately increases and decreases. The voltage across the capacitor increases according to eq. (6.1) and then decreases according to the relationship t V'=:Voef eq. 6.3 Charge- cha rge VD ID Applied 3 signal S V 11'! Capacitor g voltage '5 b ld' ITWmeforonecydel {pead T) Figure 6.2 On an oscilloscope, the time base or the magnitude of the horizontal time axis is determined by the SWEEP TIME/DIV. From this control setting, you can determine time functions for traces on the screen. For example, suppose two complete wave cycles of a stationary sinusoidal pattern cover 6.66 horizontal divisions with a SWEEP TIME/DIV setting of 5 ms/div. Then, the time for these two cycles is time 5 ms/div X 6.66 div = 33.3 ms, so the time for one cycle or the period of the wave is T : 33.3ms/2 : 16.7 ms. EQUIPMENT ' Function Generator ' Oscilloscope ' 3 capacitors (0.05uF, 0.1uF, and 0.2uF) ' 3 resistors (5kg, lOkQ, and 20kg) ' Connecting wires PROCEDURE 1. Turn on the oscilloscope and function generator. Set the function generator frequency to 100 Hz and the wave amplitude near maximum. Connect the squarewave output of the function generator directly to the vertical input terminals of the oscilloscope. XSCl Figure 6.3 2. Set up the circuit as shown in Figure 6.3 with R==R1==10k and C==C1= OlyF. 3. Adjust the time (TIME/DIV) until the rising curve extends well across :he screen. 4. The time constant is represented by the horizontal distance from the point where the trace starts to move up to the point where it crosses :he horizontal line 5 divisions up. The time is found by multiplying the horizontal distance by the TIME/DIV setting.Record in Data Table l. 5. ereat Procedures 3 and 4 with R==R2==5kQ and R==R3==20k. 6. Plot the experimental T versus R. Determine the slope of the straight line that best fits the data. 7. Replace R with R1==10k, and repeat Procedures 3 and 4 with C'=(% =(l05MF and C = C3 = 0.2MF . 8. ?lot the experimental T versus C. Determine the slope of the straight line that best fits the data. 9. Compute the time constants for each of the RC combinations using the {nown R and C values, and compare with the experimentally determined values by finding the percent errors. V. DATA AND RESULTS Table l Divisions Sweep Experiment Case R C for 0.63 time = Time Computed Percent . . RC error rise d1V constant RiC1 R2C1 R3C1 Computations: Table 2 Divisions Sweep Experiment Computed Percent Case R C for 0. 63 time = Time RC error rise div constant RIC2 R1C3 Computations : VI. CONCLUSIONS VII . QUESTIONS 1. Judging based on your experimental results, under what conditions are the charging times of different RC circuits the same? 2. When an RC series circuit is connected to a dc source, what is the voltage on a capacitor after one time constant when (a) charging from zero voltage and (b) discharging from a fully charged condition? 3. How could the value of an unknown capacitance be determined using the experimental procedures? Show explicitly by assuming a value for an experimentally determined time constant. 4. What could be a practical application of an RC circuit? 5. Can the voltage across a capacitor be measured with a common voltmeter? Explain. References : 1. Wilson, J. D., & Hernandez-Hall, C. A. (2015) . Physics Laboratory Experiments (Eight ed. ) . USA: Cengage Learning