Ohm's law - Date Grade Physics 211L Ohms Law Name_Sarah...

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Date:__08/03/2007__ Physics 211L Ohm’s Law Name: __Sarah Karam _______________________ Section number: __-1- ____________ Partner’s Name: ___Toni Kondakji _____________ Instructor: __Ms. Sarah Najm__ Part I. Computer-aided measurements A- Ohmic devices- passive resistor: Determination of the resistance using the I-V curve: R = 10 R = 33 I (A) V (V) I (A) V (V) 0.096 0.98 0.03 0.98 0.201 1.959 0.06 1.993 0.285 3.007 0.08 2.568 0.235 2.339 0.09 2.973 Use linear regression to determine the experimental value for each resistance along with its root-mean-square error. Compare the determined experimental value to the actual value of the resistance. At R = 10 Using the calculator, y = 10.634x – 0.0859 Experimental value of R = slope = 10.634 But, 2 2 N N i i i i N x x ∆ = - = 4 (0.096 2 +0.201 2 +0.285 2 +0.235 2 ) – (0.096+0.201+0.285+0.235) 2 ∆= 0.076779 e i = | y measured – y calculated | 1 Grade: 2 2 2 N i i e N N α = -
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e 1 = |0.98 – 0.934964| = 0.045036 e 1 2 = 2.028 × 10 -3 e 2 = |1.959 – 2.051534| = 0.092534 e 2 2 = 8.563 × 10 -3 e 3 = |3.007 – 2.94479| = 0.06221 e 3 2 = 3.87 × 10 -3 e 4 = |2.399 -2.41309| = 0.01409 e 4 2 = 1.985 × 10 -4 Σ e i 2 = 0.0146595 σ 2 = 2 (0.0146595/0.072732) σ = 0.635 R = 10.6 ± 0.6 % error of R = 10 : exp lit lit R R R - × 100 = 10 10.6 10 - × 100 = 6 % . Error is acceptable since it is less than 12 % . At R = 33 Using the calculator, y = 32.567x – 5.786 × 10 -3 Experimental value of R = slope = 32.567 But, 2 2 N N i i i i N x x ∆ = - = 4 (0.03 2 +0.06 2 +0.08 2 +0.09 2 ) – (0.03+0.06+0.08+0.09) 2 ∆= 8.4 × 10 -3 e i = | y measured – y calculated | e 1 = |0.98 – 0.985496| = 5.496 × 10 -3 e 1 2 = 3.0206 × 10 -5 e 2 = |1.993 – 1.965206| = 0.027794 e 2 2 = 7.725 × 10 -4 e 3 = |2.568 – 2.618346| = 0.050346 e 3 2 = 2.535 × 10 -3 e 4 = |2.973 – 2.944916| = 0.028084 e 4 2 = 7.887 × 10 -4 Σ e i 2 = 4.126406 × 10 -3 2 2 2 2 N i i e N N α = -
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σ 2 = 2 (4.126406 × 10 -3 /8.4 × 10 -3 ) σ = 0.991 R = 33 ± 1 % error of R = 33 : exp lit lit R R R - × 100 = 33 33 33 - × 100 = 0 % . Error is acceptable since it is less than 12 % . Use linear regression to determine the experimental value of each equivalent resistance along with its root-mean-square error. Compare these values to those that can be calculated from the previous measurements. For resistors in series: R eq = 43 Using the calculator, y = 42.345x + 0.0118 Experimental value of R = slope = 42.345 But, 2 2 N N i i i i N x x ∆ = - = 4 (0.045 2 +0.024 2 +0.047 2 +0.06 2 ) – (0.045+0.024+0.047+0.06) 2 ∆= 0.019484 e i = | y measured – y calculated | e 1 = |1.959 – 1.917325| = 0.041675 e 1 2 = 1.7368 × 10 -3 e 2 = |1.014 – 1.02808| = 0.01408 e 2 2 = 1.982 × 10 -4 e 3 = |1.993 – 2.002015| = 9.015 × 10 -3 e 3 2 = 8.127 × 10 -5 Resistors in series Resistors in parallel I (A) V (V) I (A) V (V) 0.131 0.98 0.045 1.959 0.201 1.554 0.024 1.014 0.259 1.993 0.047 1.993 0.302 2.331 0.06 2.534 3 2 2 2 N i i e N N α = -
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e 4 = |2.534 – 2.5525| = 0.0185 e 4 2 = 3.4225 × 10 -5 Σ e i 2 = 2.050495 × 10 -3 σ 2 = 2 (2.050495 × 10 -3 /0.019484) σ = 0.45878 R = 42.3 ± 0.5 % error of R = 43
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