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Xavier University

College of Engineering

Mechanical Engineering

Experiment Number: 3

Experiment Title: Resistors in Parallel and Series

Date Performed: August 4, 2010 Subject: ACE 03F

Date Submitted: August 18, 2010 Group Number: 7

Group Leader : Mark Julius R. Cabasan

Group Member/s: Ashton Leo Gaoiran

Mark Anthony Maraya

Duane Brose

Tracy Eduria

Presentation : ___________________

Data and Results : ___________________

Analysis and Conclusions: ___________________

Answers to Questions : ___________________

Total : ___________________

Remarks: _________________________________________________________

_________________________________________________________

_________________________________________________________

Instructor : Engr. Jose Mag-abo II

Instructors Signature: ________________________

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I. Objectives

The objective of the experiment was to determine equivalent resistances of resistors

connected in parallel and series.

II. Introductory Information

Ohms law states that the voltage across a resistor is directly proportional to the current

flowing through the resistor. The constant of proportionality is the resistance value of the resistor

in ohms. In equation form: V = IR where V is the voltage, I is the current, and R is the

resistance. The need to combine resistors in series or in parallel occurs so frequently that it

warrants special attention. The process of combining the resistors is facilitated by combining

two of them at a time. Resistors in series exclusively share a single node and consequently

share the same current.

Thus,

I = I1 = I2 = I3

R = R1 + R2 + R3

V = V1 + V2 + V3

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Resistors in parallel are connected to the same two nodes and consequently share the same

voltage.

Thus,

V = V1 = V2 = V3

I = I1 = I2 = I3

I/R = 1/R1 + 1/R2 + 1/R3

These equations are derived using Ohms law and the Kirchoffs current and voltage laws (KCL

and KVL). In the experiment, these relations are verified using different configurations of

resistors.

Reference: Fundamentals of Electric Circuits (3rd ed.) by Alexander Sadiku

http://physics.tamuk.edu/~suson/html/1402/dc.html

III. Materials Needed

The materials needed were the bread box, the digital multimeter, alligator connectors,

and 5 assorted resistors (10k, 5k, 500, 3k, and 470).

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IV. Procedure

1. Measure and record the values R1, R2, R3, R4, and R5.

2. For each configuration A to G, measure and also compute the resistance between the

free ends R1 and R5.

3. Display the results in a neat table, including the percentage difference, 200% ([Rmeasured

Rcomputed]) / (Rmeasured + Rcomputed).

Configurations:

A

R1 R2 R3 R4 R5

B R1 R2 R3 R4 R5

C R2

R1 R3 R5

R4

R1 R2

D R5

R3 R4

E R1 R2

R5

R3 R4

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R1 R4

F R2 R5

R3

R1 R2 R3

G

R4 R5

V. Data and Results

R1 = 11.9 , R2 = 386 , R3 = 2,172 , R4 = 387,100 , R5 = 68,100

Measured () Calculated () % Difference

A 459,000 457,769.9 1.5x10-3

B 11.5 11.4 8.7x10-4

C 68,300 68,439.47 -2.04x10-3

D 68,400 68,470.55 -1.031x10-3

E 70,500 68,497.49 .0288

F 395.9 393.2 6.84x10-3

G 60,500 58,335.89 .0364

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Calculations:

A. Req = R1 + R2 + R3 + R4 + R5

= (11.9 + 386 + 2,172 + 387,100 + 68,100)

Req = 458,309.9

B. 1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5

1/Req = [1/11.9 + 1/386+ 1/2,172 + 1/387,100 + 68,100] (1/)

Req = 11.49

C. Req = R1 + [R2R3R4]/[R3R4 + R2R4 + R2R3] + R5

Req = {11.9 + [386 (2,172) (387,100)] / 2,172 (387,100) + 386 (387,100) + 386 (2,172)] +

68,100} k

Req = 68,439.47

D. Req = R1R3/(R1+R3) + R2R4/(R2+R4) + R5

= {[11.9 (2,172)/ (11.9 +2,172)] + [386 (387,100)/ (386+387,100)] + 68,100} k

Req = 68,470.55

E. Req = (R1+R2)(R3+R4)/(R1+R2+R3+R4) + R5

= {(11.9 +386) (2,172+387,100)/ (11.9 +386+2,172+387,100) + 68,100} k

Req = 68,497.49

F. Req = [R1R2R3]/[R2R3 + R1R3 + R1R2] + R4R5/ (R4 +R5)

= 11.9 (386) (2,172)/ [386 (2,172) +11.9 (2,172) +11.9 (386)] + 387,100 (68,100)/

(387,100+68,100)

Req = 393.2

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G. R = R2 + R3(R5)/ (R3+R5)

= 386+ 2,172 (68,100)/ (2,172+68,100)

R = 5.172 k

Req = R1 + R4R/ (R4 + R)

= 9.75 + 2.96(5.172)/(2.96+5.172)

Req = 58,335.89

VI. Analysis and Conclusion

Based on the experimental data, the % differences are 0.00150, 0.000870, 0.00204,

0.001031, 0.0288, 0.00684 and 0.0364 for configurations A, B, C, D, E, F and G respectively.

The average percent difference = 0.011%. Thus, the measured and calculated values for

resistances are close to each other. The calculated values are derived from theoretical

considerations of resistors in series and parallel. The equations used in the calculations are

rooted in the use of Ohms law and Kirchoffs current and voltage laws (KCL and KVL).

To sum up, the relations for calculation of resistances for resistors in series and parallel

are verified. In general, for resistors in series, Req = Riand for resistors in parallel, 1/Req =

(1/Ri) where Req = equivalent resistance and Ri = individual resitance.

Mark Julius R. Cabasan

BSME-3