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Capacitor RUSTIA, PRINCE LORD, J.,SAN JUAN, CAMILLE, R.,SANTIAGO, ARNEL II, C. SEMILLA, CHEYENE DARIANE, B.,TORRES, JAMES ANTHONY, C.,VELASCO, MA. CARMINA, C. Thursday 2:00-5:00PM / OZ308 Mathematics and Physics Department, Adamson University Abstract The purpose of the laboratory experiment is to describe the charging and discharging process of the capacitors and to differentiate the charging and discharging of various capacitors. In this experiment, a capacitor is charged by connecting it to a source and is also discharged by immediately disconnecting the source from the circuit. The time taken is recorded at uniform interval. The graph of charging and discharging capacitors are both in exponential form. However, they are contrasting in direction. Therefore, capacitance is the maximum charge that a capacitor can store. The stored energy of the capacitor, nevertheless, is not always equal to its capacitance 1. Introduction Capacitors are devices that can store electric charge and energy. A capacitor can be gradually charged to the necessary voltage and after that released rapidly to provide the energy required. A capacitor consists of two conductors isolated by a small separation. At the point when the conductors are associated with a charging device (for instance, a battery), charge is exchanged from one conductor to the next until the distinction in potential between the conductors due to their equivalent, however opposite charge noticeably equivalent to the potential difference between the terminals of the charging device. The amount of charge stored on either conductor is specifically corresponding to the voltage, and the consistent of proportionality is known as capacitance. The aim of this experiment is to compare the charging and discharging process of different capacitor.

potential across the capacitor increases which is known as the charging process of the capacitor. However, when the switch is open and the circuit is shorted, the potential across the capacitor approaches to zero which is known as the discharging process of the capacitor. A resistor in series is used to absorb the heat that maybe generated in the process. Mathematically, the voltage across the capacitor at any given time is derived:

2. Theory

3. Materials and Procedure

A capacitor is a device which consists of parallel conductors separated by an insulating material. It can store energy by transferring charges from a conductor to another. To move charges between the conductors, work must be done through the resulting potential difference from the conductors. The magnitude of charge stored is directly proportional to the potential difference between the conductors. The ratio of Charge Q to potential difference or Voltage V is constant known as the Capacitance C. Mathematically,

C = Q/𝑉 Where C is the capacitance in Farad (F), Q is the magnitude of charge in Coulomb (C), and V is the Voltage or potential difference in Volt (V) when a capacitor is connected to a DC source, charges move to the plates and the

Where VO is the maximum voltage in Volt, tis the time in seconds, R is resistance in series with capacitor in Ohm, and C is the capacitance of the capacitor in Farad. The potential difference across the capacitor that reached 63% of the maximum value of voltage VO is at t = RC which is known as Time Constant or the relaxation time which measure how quickly the capacitor charges.

4. Results and Discussion Table 1 presents the data gathered by the students in the experiment proper. Table 1. Charging and Discharging of Capacitor

C = 470 µF

C = 100 µF

Time Voltage (V) Voltage (V) Voltage (V) Voltage (V) (Charging (Discharging (Charging (Discharging (s) 5 10 15

Process)

Process)

Process)

Process)

0.5 1.9 2.6

5.0 4.1 3.5

3.1 5.0 5.9

3.5 1.5 1.0

7 6 5 4 3 2 1 0

470 µF 100 µF

5 10 15 20 25 30 40 50 60 70 Time (s)

Figure 1. Charging process of the capacitor Figure 1 shows the difference between 470 µF and 100 µF capacitor in charging process. 470µF capacitor charged slower than a 100 µF capacitor. This is because higher capacitance has higher value of time constant so it will take a longer time to charge a capacitor with higher capacitance than with lower capacitance.

6 5

Voltage (V)

3.2 3.0 6.0 0.5 3.9 2.5 6.4 0.4 4.3 2.1 6.4 0.4 4.9 1.5 6.5 0.0 5.2 1.1 6.5 0.0 5.6 1.0 6.5 0.0 6.0 0.4 6.5 0.0 The students used two values of capacitor in a RC circuit. The capacitors was charged for 70 seconds using a DC power supply and discharged. The 470 µF capacitor stored an approximate amount of 6.0 V after 70 seconds while the 100 µF capacitor stored 6.5 V. In the discharging process, the 100 µF capacitor discharged a lot faster than the 470 µF capacitor. Since the RC time constant is the product of the resistance and capacitance, higher capacitance will result to higher time constant and makes charging and discharging slower. The computed potential V at 25 seconds for 470 µF capacitor is 4.1 V and 9.2 V for 100 µF capacitor. The group obtained a 4.9% error in the first trial while 30.4% error in the second. The errors may be due to inconsistency and inacuracy on the measuring instrument and human error.

Voltage (V)

20 25 30 40 50 60 70

4 470 µF 100 µF

3 2 1 0 5 10 15 20 25 30 40 50 60 70 Time (s)

Figure 2. Discharging process of the capacitor Figure 2 shows the difference between 470 µF

and 100 µF capacitor in discharging process. The 100 µF discharged faster than 470 µF also because of the value of the time constant. Capacitors with lower capacitance will discharge faster than higher capacitor in a RC circuit. 5. Conclusion References 1. Caῆares, A., Casquejo, E., Ching, M., Fadri, R., Laban, R., Miranda, M., Siguenza, R., Turnbull, W. (2017). Physics Laboratory Manual Volume 2. 2. Charging and Discharging of Capacitor. Retrieved from http://www.academia.edu/11679388/Charging_a nd_Discharging_of_a_Capacitor_Lab_Report 3. Physics Laboratory Manual