Experiment EC3: RC CircuitsIn this experiment you will accomplish the following tasks:1) Study the charging of a capacitor through a resistor.2) Study the discharging of a capacitor through a resistor.3) Study the way capacitance adds in both series and parallel arrangements.Consider the circuit above. In (a), the capacitor is uncharged and nocurrent flows because the switch is open. In (b), current begins to flowcharging the capacitor. As the charge q(t) builds over time on the capacitor, the voltage across it also increases.As the voltage across the capacitor increases, the voltage across the resistor decreases.V-1 Charging through a resistorAs charge builds up on the capacitor,the voltage across the resistor decreases.The voltage across the resistor is givenby:tRVeTaking the natural logarithm of both sides of this equation gives:ln lnRtVThe time constant is given by = RC.You will charge the 1.00 F capacitor through a 100  resistor using the circuit shown on the next slide.Momentarily discharge the capacitor by connecting the + and –terminals together for approximately 10 seconds.Using the DVM, set the power supply voltage to 4.9 – 5.0 volts.This is to prevent exceeding the rated voltage of the capacitor. Once you have set the voltage, do not re-adjust it.Open the knife switch and wire the circuit as shown. Make certain the polarity of the power supply is correct to prevent damage to the capacitor.Close the knife switch by placing it in the “Discharge” position and start the timer simultaneously. Record the voltage indicated by the DMM every 20 seconds for 3 minutes.Allow the capacitor to charge until the DMM reading decreases to approximately 0.4 volts.ln lnRtVcomparewith the slope-intercept from of a line yb sxVI-1 of the reportA plot of lnRVvs t will have a slope s = 1Tabulate the data from V-1. Your table should include columnsfor , VRand time Plot vs t. From s and sof this plot, determine and report ±.lnRVlnRVV-2 Discharging through a resistorAs the capacitor discharges, the current flowing in the circuit decreases. This causes the voltage across the resistor to decrease.The voltage across the resistor is givenby:tRVeTaking the natural logarithm of both sides of this equation gives:ln lnRtVThe time constant is given by = RC.You will discharge the 1.00 F capacitor through a 100 resistor using the circuit shown at left.After allowing the DMM reading to decrease to approximately 0.4 Volts, open the knife switch.Disconnect the leads to the power supply by removing them from the front of the power supply. Connect these two leads together.Close the knife switch by placing it in the “Discharge” position and start the timer simultaneously. Record the voltage indicated by the DMM every 20 seconds for 3 minutes.ln lnRtVcomparewith the slope-intercept from of a lineybsxVI-2 of the reportA plot of lnRVvs t will have a slope s = 1Tabulate the data from V-2, plot vs t. From s and sof this plot, determine and report ±.lnRVCompare the time constant determined from charging with the time constant determined by discharging.V-3 and V-4: different resistorYou will now charge/discharge the capacitor through a 220 resistor. This is done in the same manner as sections V-1 and V-2. You will connect the + of the capacitor as shown below.VI-3 and VI-4 of the reportThe analysis for VI-3 is carried out in the same manner as for VI-1Similarly, the analysis for VI-4 is carried out in the same manneras for VI-2.V-5 Series and Parallel combinations of capacitorsMeasure and record the capacitance of CAand CBusing the DMMset to the 20 nF scale.Connect CAand CBin a series arrangement and using the DMMmeasure and record the capacitance of this combination.Connect CAand CBin parallel and using the DMM measure andrecord the capacitance of this combination.VI-5 of the reportCalculate the expected value for CAand CBin a series arrangement.Compare this to the DMM of the series combination of thesecapacitors.Calculate the expected value for CAand CBin a parallel arrangement.Compare this to the DMM of the parallel combination of