University:
Borough of Manhattan Community College
Course:
PHY 110 | General Physics
Academic year:

2023
Views:

330

Pages:

9
Author:

Carina Becker

The RC Time Constant The purpose of this laboratory is to examine the charging and discharging process of capacitors in a RC circuit and determine their time constants. All RC and DC circuits contain a source of electromotive force, resistors, and capacitors .However, in contrast to DC circuits without capacitors, the currents of RC circuits take some time to reach their constant values. This time is the time needed to charge the capacitors within RC circuits and is known as the time constant t. For a basic RC circuit containing one resistor of resistance ‘R’, one capacitor of capacitance ‘C’ and one source of electro motive fore ‘ E’, the Time constant can be expressed using the following equation : t=R * C During the charging process the voltage across the capacitor Vc increases with time t from zero to Ɛ . The voltage across the capacitor can be determined using the following equation: It will take an infinite amount of time for the capacitor to fully charge to its maximum Value, when a fully charged capacitor is discharged through a resistor by putting the switch the voltage across the capacitor decreases with time. The voltage V as a function of time t is given by: ΔV(t)=ΔV0e^(-t/r) After a time t=τ=RC (one time constant), the voltage across the capacitor has decreased to a value: ΔV(t=RC)=0.3ΔV0 Taking the natural logarithm (base e): Ln(ΔV(t))=-t/RC+lnΔV0 Table 1 Table 2 3 2 1 LnΔV) 0 -1 0 10 20 30 40 50 60 ln(del(v-v0)) Linear (ln(del(v-v0))) -2 -3 -4 -5 Time(s) In this experiment, charging and discharging of the capacitor with different resistors were observed. The main goal was to charge up the capacitor. For this, the circuit that we used included the resistor and the capacitor with the power supply. To extend the charging process, the resistors were used. In result, we saw that as capacitor was being charged we saw an increase in the voltage. Thus, the increasing phase represents charging of the capacitor and decay represents the discharging. Time constant was also taken account to represent the relation between the time constant, the resistance, and the capacitor. The time constant shows how long it takes to charge up the capacitor. As time constant increase, the voltage reaches the maximum voltage of the capacitor. Time constant matched theoretically, found by doing 1/c from the statics box, and experimentally. The purpose of this experiment was achieved because the charging and discharging was observed with the expected results. The charging showed the exponential increase and the discharging showed the decay. The value of capacitance was found using the statics box from the graph. Thus, it shows that the charging and discharging.