DC Circuit LAB Report 4 DC Circuit (Series and Parallel) PDF

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Tittle/Objectives/ Theory/Procedure/ Units (3 M) Data entry (3 M)

UNIVERSITI TEKNOLOGI MARA KAMPUS JENGKA

FUNDAMENTAL OF PHYSICS, ELECTRICITY, MAGNETISM AND OPTICS LABORATORY REPORT Exp. No.

DC Circuit (Series and Parallel) 2

Date of experiment

11/6/2020

Date of report submission

26/6/2020

Name Matrix No. Name of lecturer

SITI NURSYAFIQAH BINTI ZARIMAN 2019207852

Group

Madam Nur Sha’adah binti Zainuddin

*Graph analysis (3M) Answer to Question (3 M)

PHY 443

Title of experiment

Data Manipulation (3 M)

AS203A

Discussion and Conclusion (3 M)

TOTAL (18)

OBJECTIVE 1. To study the concepts of potential difference, electric current and resistance. 2. To study the Ohm’s law and its application in series and parallel circuits.

APPARATUS AND MATERIALS DC Power supply, connecting wires, Resistor 5 𝛺,10 𝛺,15 𝛺, digital ammeter and voltmeter, DC ammeter and circuit board containing switch, fuse, resistor based.

THEORY The electric potential difference or voltage, V between two points is the work per unit charge required to move a charge between the points. The voltage is usually denoted by ∆𝑉 and has units of volts, joules per Coulomb. Voltage denotes the work per unit charge that must be done against a static electric field to move a charge from one point to another. It may represent a source of energy, lost, stored or used energy. The electric current or current, I is the charge that flows per unit time. It is usually measured in ampere. An ampere is a coulomb per second. It is conventional to speak of the current as the flow of positive charge in a circuit. Ohm’s law states that the potential difference across a conductor, V is directly proportional to the current ,I and the temperature are constant. 𝑉 = 𝐼𝑅 ……….(1) R is the resistance and is measured in ohms. An ohm is a volt per amper

Resistors connected in Series.

Figure 1: Resistors connected in Series When a resistors is connected in series as shown in Figure 1, the current is the same throughout the circuit. 𝐼𝑡 = 𝐼1 = 𝐼2 = 𝐼3 ……….(2) Kirchhoff’s Law states that; 𝑉𝑡 = 𝑉1 + 𝑉2 + 𝑉3 ……….(3) The equivalent resistance, Re, of a number of resistors connected in a series is equal to the sum of the individual resistances. 𝑅𝑡 = 𝑅1 + 𝑅2 + 𝑅3……….(4) Resistor connected in Parallel

Figure 2: Resistors connected in parallel

PROCEDURE Part A: For Series Circuit

Figure 3: Series Circuit 1. The 𝑅1, 𝑅2, 𝑅3 and the ammeter was connected in series as shown in Figure 3. The voltmeter was connected across point A and B. The DC power was set on 0-15 volt and the know was arrange to o give 𝑉𝐴𝐵 of 0,1,2,3,4, and 5 volts. The current I was determined for every corresponding voltage. The values was recorded on a table. 2. A graph of V against I was plotted and the best fit line was drew to represent the data. The total resistance was determined from the graph. 3. The power supply was set at 2V and the current across each resistors and the voltage dropped across each resistors as 𝑉1, 𝑉2 and 𝑉3 were measured and recorded. 𝑅1, 𝑅2 and 𝑅3 were calculated and the values were recorded thoroughly. 4. The value of 𝑅𝑇 was calculated by using equation (4) and the calculated values of 𝑅1, 𝑅2, and 𝑅3 from step 3. 5. The error calculated was compared to the value

Part B: For Parallel Circuit

Figure 4: Parallel Circuit

1. 𝑅1, 𝑅2 and 𝑅3 connected with ammeter to calculate and measure the total current. Al voltmeter were also connected across point A and B.The DC power supply was set on 0-15 volt range and the knob was adjusted to give VAB of 0, 1, 2, 3, 4, and 5 volts. The current, I for the every corresponding voltage were determined and the values were recorded in a table. 2. A graph of V against I was plotted and the best fit line was drew to represent the data. The total resistance was determined. 3. VAB was set at 0.5 volts and the ammeter was connected to measure the individual current through 𝑅1, 𝑅2 and 𝑅3. These values along 𝑉1, 𝑉2 and 𝑉3 were recorded. 4 4. . The 𝑅𝑡 was calculated by using equation (7) and calculated values of 𝑅1, 𝑅2 and 𝑅3 from step 3. The value calculated from step 4 was compared with the value calculated from step 2. 5. The error calculated was compared to the value.

DATA 𝑅1 = 5 Ω 𝑅2 = 10 Ω 𝑅3 = 15 Ω a) Series circuit

Vab

Curent/ I (A)

Voltage (V)

1

0.03

1

2

0.07

2

3

0.1

3

4

0.14

4

5

0.17

5

Vt = 2V, I= 0.07A Resistors R1 R2 R3

Current /I (A) 0.07 0.07 0.07

Voltage (V) 0.33 0.67 1.00

Graph of V against I 6 y = 46x - 1.41

5

y = 21.522x + 0.6757

Voltage, V

4 y = 28.502x + 0.0928

3 2 1 0 -0.05

0 -1

0.05

0.1

Current, I

Graph of Voltage against Current for Series circuit 𝑦 = 𝑚𝑥 + 𝑐 𝑉 = 𝐼𝑅

0.15

0.2

0.25

𝑅=

𝑉 =𝑚 𝐼

∴ 𝑅 = 28.50Ω

Uncertainty of R, ∆𝑅

∆𝑅 = ∆𝑚 =

𝑀𝑚𝑎𝑥 −𝑀𝑚𝑖𝑛 2

46.00−21.52

∆𝑚 =

2

∆𝑚 = ±12.24Ω ∴ 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑅 𝑖𝑠 (𝑅 ± ∆𝑅) = (28.50 ± 12.24)Ω For series circuit:

R1 =

0.33

R2=

0.07

= 4.71Ω

0.67 0.07

= 9.57 Ω

R3=

1.00 0.07

= 14.29 Ω

𝑅 𝑇 = 𝑅1 + 𝑅2 + 𝑅3 = (4.71 + 9.57_14.29)Ω = 28.57 Ω ∴ 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑅 𝑖𝑠 28.57Ω

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 =

| 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒| 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 =

× 100%

| 28.50 − 28.57| × 100% 28.50

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 = 0.24%

b) Parallel Circuit Vab

Curent/ I (A)

Voltage

1

0.37

1

2

0.37

2

3

1.10

3

4

1.47

4

5

1.83

5

V= 0.5V Resistors R1 R2 R3

Current /I (A) 0.10 0.05 0.03

Voltage (V) 0.5 0.5 0.5

Graph V against I 7 6

y = 3.326x - 0.0865

Voltage, V (V)

5

y = 2.7448x + 0.0393

4 y = 2.7322x - 0.0054 3 2 1 0 -1

0

0.5

1

Current, I (A)

Graph of Voltage against Current for Series circuit 𝑦 = 𝑚𝑥 + 𝑐 𝑉 = 𝐼𝑅 𝑅=

𝑉 =𝑚 𝐼

∴ 𝑅 = 2.73Ω

1.5

2

Uncertainty of R, ∆𝑅

∆𝑅 = ∆𝑚 =

𝑀𝑚𝑎𝑥 −𝑀𝑚𝑖𝑛 2

2.74−3.33 2

∆𝑚 =

∆𝑚 = ±0.30Ω ∴ 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑅 𝑖𝑠 (𝑅 ± ∆𝑅) = (2.73 ± 0.30)Ω For parallel circuit: R1=

0.5 0.10

= 5.00 Ω

𝑅2 =

0.5

0.5

𝑅3 = 0.03

0.05

=10.00 Ω

= 16.67 Ω

𝑅 𝑇 = 𝑅1 + 𝑅2 + 𝑅3 = (5.00 + 10.00 + 16.67)Ω = 31.67 Ω 1 1 1 1 + + = 𝑅1 𝑅2 𝑅3 𝑅𝑇 1 1 1 1 = + + 5 10 16.67 𝑅𝑇 𝑅𝑇 = 2.78 Ω Experimental value of R is 2.78 Ω

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 =

| 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒−𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒| 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 =

× 100%

| 2.73 − 2.78| × 100% 2.73

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 = 1.0%

DISCUSSION For series circuit, the theoretical value of the equivalent resistance is (𝑅 ± ∆𝑅) = (28.50 ± 12.24)Ω . The current is set to the value of 0.07A, therefore we get the experimental value of equivalent resistance obtained is 28.57 Ω. The percentage error obtained from this experiment is 0.24%. In series circuit connection, the current that flows in and out of the components are respectively the same however the voltage is different. Thus, if one circuit is broken at any point, no current will flow to the circuit. While for parallel series, the theoretical value of the equivalent resistance is (𝑅 ± ∆𝑅) = (2.73 ± 0.30)Ω. When the voltage is set to the constant value of 0.5, the experimental value of equivalent resistance that obtained is 2.78 Ω. Thus, the percentage error that obtained from this experiment is 1.0% As we know, in the parallel circuit, the value of voltage (V) will be the same across each component of the parallel circuit and the sum of the currents through each path is equal to the total current that flows from the source. Therefore when one of the parallel path is broken, the current will still be flowing in the other path. There are some errors that might slightly effect the percentage error, one of the errors is the wire have their own value of resistance. Besides that, internal resistance also exist in the voltage source,in conjuction with the formula of 𝜀 = 𝐼𝑟 + 𝑅.

CONCLUSION For series circuit, the percentage error obtained is 0.24%. The behaviour of the series circuit is the current, I is the same across each component and the voltage applied to a series circuit is equal to the sum of the individual voltage drops in each resistors. Thus, the experiment is successful due to the percentage error. For parallel circuit, the percentage error obtained is 1.00%. The behaviour of the parallel circuit is the voltage, V is the same across each component of the parallel circuit and the sum of the currents through each path is equal to the total current that flows from the source.. Therefore it is also successful due to the percentage error that obtained. In conlusion, we learned the concepts of potential difference, electric current and resistance. Besides that, we could study and use the Ohm’s law and saw the application in series and parallel circuits.

REFERENCES 1. “Ag Power Web Enhanced Course Materials (Series Circuits)”, Retrieved 29 December 2016, from https://www.swtc.edu/Ag_Power/electrical/lecture/series_circuits.html

2. Charles Hooge (Aug 22, 2016) 20.2 Ohm’s Law: Resistance and Simple Circuits Retrieved by https://pressbooks.bccampus.ca/physics0312chooge/chapter/20-2-ohms-lawresistance-and-simple-circuits/...