Capacitor charge and discharge in parallel and series 2299130 PDF

Preview

Summary

Download Capacitor charge and discharge in parallel and series 2299130 PDF

Description

Running Head: CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES

Your Name

Date

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 1

Summary The lab was conducted successfully and various conclusions drawn. Various measurements were taken. These included the value of the capacitors as well as the voltage across the capacitors I both series and parallel connection. The charging and discharging of the capacitor was also observed, recorded and analysed. The observations were in line with theory since the charge and discharge voltages were exponential in time, having a time constant of RC. A couple of observations were also made with regard to parallel and series connection of capacitors. For capacitors connected in parallel, the equivalent capacitance is obtained by adding the individual capacitance together. For capacitors connected in series, the inverse of the equivalent capacitance is obtained by adding the inverse of individual capacitance together. For capacitors connected in series, the voltages across each capacitor is different but charge I the same. For capacitors connected in parallel their voltages are the same, but their charges are different.

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 2

List of Contents Summary.....................................................................................................................................................1 Objectives.................................................................................................................................................... 3 Introduction................................................................................................................................................. 3 Apparatus....................................................................................................................................................5 Method........................................................................................................................................................ 5 Results and Analysis....................................................................................................................................8 Discussion.................................................................................................................................................. 11 Conclusions................................................................................................................................................11 Bibliography...............................................................................................................................................12

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 3

Objectives The experiment aimed at investigating the properties of capacitor charging and discharging through a resistor. Another objective was to come up with an understanding of the capacitors connected in parallel and in series as well as the relationship between voltage, capacitance and charge. The experiment also aimed at illustrating the use and operation of function generators and oscilloscopes.

Introduction A capacitor is a passive electrical component which stores electric energy. Two parallel metallic surfaces make up a parallel-plate capacitor. Each of the two metallic plates has area A, and they are separated by a layer of insulation which has thickness d (Karady et al., 1993). The capacity of the capacitor I given by the following equation; C=ε O k

A d

Where; C represents the capacitance, in Farads. A represents the area of the individual plates in m 2 . d is the thickness of the dielectric (insulation) m, ε O is the permittivity of a vacuum(free space) for propagation of an electric field expressed in Farads/meter (F/m) k is the dielectric constant, dependant on the insulation layer material. The material of the plates does not affect capacitance. The relation of the dielectric constant ε O to Coulomb’s constant k is given in the equation below;

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 4

εO =

1 =8.85 x 10−12 F /m 4 πk

A capacitor can be manually charged by connecting it to a battery and discharged by switching this connection to for it to discharge through the resistor (Ye and Cheng, 2015). The resistor also governs the rate of charging of the capacitor.

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 5

Part of the circuit is represented above. The capacitor is uncharged at t = 0. Closing the switch allows the flow of electrons from the battery’s negative pole to the capacitor’s lower plate. These electrons are then distributed all over the plate, making it negatively charged. The free electrons on the upper plate are then repelled and they flow to the battery’s positive pole. As a result, the upper plate assumes a positive charge. The charging process takes some time. As charging begins, current is at the maximum value, this value decreases as charge is accumulated at the capacitor plates (Hinago and Koizumi, 2012). The capacitor is storing no charge at the beginning, hence it has zero voltage across it. With charge building up on its plates, the voltage increases. Capacitor voltage VC, asymptotically tends towards the voltage of the battery V bat. The exponential equations given in the table below are obeyed by the voltage across the capacitor during charging and discharging.

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 6

Apparatus Power Supply Signal Generator Oscilloscope 820Ω Resistor 1µF Capacitor

Method

Results and Analysis

Charging = V s x (1 - e-1) = 0.632 = 63.2%

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 7

Discharge = V o x e-1 = 0.368 = 36.8%

Charging cycle; V i=10 V p − p

R=820 Ω

C=1 μF

N*Time

Theoretical Exponential

Voltage Vc

constant (ms)

term (1 -

(Volts)

Experimental Measured time constant (ms)

Voltage Vc (Volts)

−n

ORC = 0.00 1RC = 0.82 2RC = 1.64 3RC = 2.46 4RC =3.28 5RC = 4.10 Discharging cycle

e ) 0.00 0.63 0.86 0.95 0.98 0.99

0.00 6.30 8.60 9.50 9.80 9.90

N*Time

Theoretical Exponential

Voltage Vc

constant (ms)

term (1 -

(Volts)

−n

e

ORC = 0 1RC = 0.82 2RC = 1.64 3RC = 2.46 4RC =3.28 5RC = 4.10

3.67 1.35 0.49 0.18 0.06

6.4 9.0 9.6 10 10

Experimental Measured time Voltage Vc constant (ms)

(Volts)

) 3.80 0.80 0.50 0.18 0.00

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 8

Calculate the Capacitance value of C3 and C4 in parallel

=

C3 / 4=C 3 + C 4 C 3 / 4=4.7 μ F +6.8 μ F

C3 / 4=11.5 μ F Calculate the Top row of capacitors (CTop Row) which are all in series = 1 C Top Row 1 C Top Row 1 C Top Row

=

1 1 1 + + C1 C 2 C 3 / 4

=

1 1 1 + + 10 μ F 6.8 μ F 11.5 μ F

=0.1+0.1471 + 0.087

1 =0.3341 C Top Row CTop Row =

1 0.3341

CTop Row =2.993 μ F Finally, calculate the Total capacitance, including C5

=

CTotal =C Top Row +C 5 C Total =2.993 μ F+3.3 μ F

CTotal =6,293 μ F Calculate the Charge in C5 (QC5 = 12v x 3.3µF)

=

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 9

Q C 5=V x C 5 Q C 5=12 V x 3.3 μ F

Q C 5=39.6 μ C Calculate the Charge in the Top capacitors (CTop Row x 12v) Q C 5=V x C Top Row Q C 5=12 V x 2.993 μ F

Q C 5=39.6 μ C Measure the voltages across each capacitor and record your values: VC1 = …..., VC2 =…..., VC3 =……, VC4 = ……, VC5 =…… Calculate the charge in each capacitor using your voltages: QC1 =……, QC2 =……, QC3 =……, QC4 =……, QC5 =……

Discussion A capacitor’s charge-voltage formula is; Q = CV. For capacitors connected in parallel, the equivalent capacitance is obtained by the equation C Equivalent=C 1 +C2 + C 3 … For capacitors connected in series, the equivalent capacitance is obtained by the equation. 1 1 1 1 = + + … C Equivalent C 1 C2 C 3 For capacitors connected in series, the voltages across each capacitor is different but charge I the same as shown in the following equation;

Q T =Q 1+Q 2+ Q 3 …

For capacitors connected in parallel their voltages are the same, but their charges are different.

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 10

Conclusions Various measurements were taken. These included the value of the capacitors as well as the voltage across the capacitors I both series and parallel connection. The charging and discharging of the capacitor was also observed, recorded and analysed. The observations were in line with theory since the charge and discharge voltages were exponential in time, having a time constant of RC. A couple of observations were also made with regard to parallel and series connection of capacitors. For capacitors connected in parallel, the equivalent capacitance is obtained by adding the individual capacitance together. For capacitors connected in series, the inverse of the equivalent capacitance is obtained by adding the inverse of individual capacitance together. For capacitors connected in series, the voltages across each capacitor is different but charge I the same. For capacitors connected in parallel their voltages are the same, but their charges are different.

Bibliography Hinago, Y. and Koizumi, H. (2012). A Switched-Capacitor Inverter Using Series/Parallel Conversion With Inductive Load. IEEE Transactions on Industrial Electronics, 59(2), pp.878-887.

CAPACITOR CHARGE AND DISCHARGE IN PARALLEL AND SERIES 11

Karady, G., Ortmeyer, T., Pilvelait, B. and Maratukulam, D. (1993). Continuously regulated series capacitor. IEEE Transactions on Power Delivery, 8(3), pp.1348-1355. Ye, Y. and Cheng, K. (2015). Modeling and Analysis of Series–Parallel Switched-Capacitor Voltage Equalizer for Battery/Supercapacitor Strings. IEEE Journal of Emerging and Selected Topics in Power Electronics, 3(4), pp.977-983....