Ohms lab

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California State University, San Marcos *

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101

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Electrical Engineering

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Apr 3, 2024

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pdf

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Resistance and Ohm’s law Introduction Electrical resistance is the resistance offered by a material to the flow of electrons. Resistance is measured in Ohms ( Ω ). Resistance depends on the geometry of the material as well as an intrinsic material property called resistivity . ρ The resistivity of copper is 1.68 x 10 -8 ohm-m. This means both a short copper wire and a long copper wire have this same value of resistivity. The resistivity of glass is about 10 +14 ohm-m; since this is magnitudes larger than that of copper, glass resists the flow of current through it (an insulator) far more than copper (a conductor). Metals like copper, silver, aluminum have low resistivity, making them good conductors and are used to make wires. When resistance is large, the current is small. Also, a large resistance means electrical energy is wasted as heat. In terms of length L, cross-sectional area A, and resistivity the electrical ρ, resistance R (at constant temperature), is given by 𝑅 = ρ 𝐿 𝐴 Go to: https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html or Google PHET HTML5 Physics- Resistance in a wire Play with the PhET and familiarize yourself with the simulation. 1 GES101 online SC Fall2020

Resistance 1. Adjust the three variables in the simulation to find the maximum and minimum possible value of resistance in ohms. R max = 2,000 ohms R min = 0.0001 ohms Q 1. How is it possible to decrease the resistance of the sample without changing the material it is made of? (Hint: there are two ways of doing so. For each one express whether you increase or decrease the variable)) - one way to decrease the resistance of the sample without changing the material it’s made out of decreasing the resistivity. we can decrease the length or decrease the area, and this would decrease the resistance of the sample. 2. Adjust values of L, A and in the sim to obtain a resistance of 1ohm. ρ = 0.50 A = 6.42xm^2 L = 12.84 ρ 3. Plug the values you selected on 2. in the formula for resistance and calculate the resistance using a calculator. Show your work below. R = 1 Resistance versus Length 4. Adjust the resistivity pointer at the midpoint (0.50 Ω.cm) and the area pointer at 7.50 cm 2 . 5. Keep the length of the wire at 2 cm and note the resistance R in Table 1. Note : sometimes in this simulation you cannot select the exact value you want. Don’t worry about that. Select the closest value you can. 2 GES101 online SC Fall2020

6. Repeat by increasing the length of the wire by 2 cm each time until you fill table 1. Resistivity ρ = 0.5 Wire area A= 7.5 cm^2 Table 1: How wire length affects resistance Q3. If you increase the length of a wire, will its resistance increase, decrease or stay the same? - the resistance will increase as the length of the wire increases . Q4. If you double the length of a wire its resistance will _________ by a factor of_______. (increase, decrease ) (2,3, 4,5) - increase by a factor of 2. Q5. If you cut an aluminum wire in half, how will the resistance of one of the pieces change? - if we cut an aluminum wire in half, the resistance of one of the pieces will decrease and be less than what it was when it was whole. Q6. If you cut an aluminum wire in half, how will the resistivity of one of the pieces change? - if we cut an aluminum wire in half, the resistivity will remain the same. Resistance versus Area 7. Adjust the resistivity at the midpoint (0.50 Ω.cm) and the length at 10 cm. 8. Select the area of the wire around 2 cm 2 and note resistance R in table 2. 3 GES101 online SC Fall2020 Length L (cm) Resistance R (Ω) 1. 2 cm 0.133 2. 4 cm 0.267 3. 6 cm 0.400 4. 8 cm 0.536 5. 10 cm 0.666 6. 12 cm 0.800 7. 14 cm 0.935

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9. Increase the area of the wire by 2 cm 2 each time until you fill table 2 and record the resistances. Resistivity ρ = 0.5 Ωcm Wire length L= 10 cm Table 2: How cross-sectional area affects resistance # Area A (cm 2 ) Resistance R (Ω) 1. 2 cm 2.50 2. 4 cm 1.23 3. 6 cm 0.833 4. 8 cm 0.624 5. 10 cm 0.500 6. 12 cm 0.416 7. 14 cm 0.357 Q7. If the cross-sectional area of a wire is decreased will the resistance increase, decrease or stay the same? - if the cross-sectional area of a wire is decreased, then the resistance will increase. Q8. A wire of uniform cross-section has a resistance = X. What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the area? Justify your answer. - the resistance of a wire decreases when the area is doubled. the resistance of a wire decreases when the length is doubled. this would balance out making the resistance constant. Q9. Silver has lower resistivity as compared to copper. If the same potential is applied across a silver wire and a copper wire of the same length and area, in which case more current will flow? Explain your answer. - more current would flow in the silver wire than the copper wire. the resistivity of a wire does not change regardless of its length or area. since the silver wire has more free electros than copper, its resistivity would be less than copper. 4 GES101 online SC Fall2020

Ohm’s Law Ohm’s law relates the current (I) flowing through a conductor, with the applied voltage-difference (V) and the resistance (R), at a given temperature. It is given as V = I R Go to https://phet.colorado.edu/sims/html/ohms-law/latest/ohms-law_en.html or Google PHET physics HTML 5 Ohm’s Law When a voltage is applied across a conductor, there will be a current flowing through it. The amount of current depends on the resistance of the conductor and it can be calculated using Ohm’s law. 1. Keep the resistance R constant at 500 ohms. Vary the voltage and observe how the current changes. 2. Keep the voltage V constant at 4.5v. Vary the resistance and observe how the current changes. Q1. State whether True or False . a. The current in a conductor increases if resistance is increased. ( false) b. If voltage is increased, the current increases as well. (true) c. If resistance is decreased, then the current increases. (true) d. The current in the resistor does not depend on resistance. (false) e. If the voltage is increased both current and resistance change. (false) 3. Keep voltage constant at values shown in the table and vary resistance to measure current and fill your data in the table. 5 GES101 online SC Fall2020

Table 3. Measured current for varying resistances # Voltage (v) Resistance (ohms) I (mA) 1 3 200 15.0 2 3 400 7.5 3 3 600 5.0 4 3 800 3.8 5 6 200 30 6 6 400 15 7 6 600 10 8 6 800 7.5 Q2. Observe the trend in your data. a) When the resistance is doubled, how does the current change? (Does the current halve, double, triple….) - the current is cut in half when the resistance is doubled. b) When the resistance triples, how does the current change? - the current is cut in thirds when the resistance is tripled. Q3. Why is the current in #2 and in #6 not the same? (R= 400 ohms in both cases) - even though the value of R is 400 in both cases, the current in #2 is different from the current in #6 because the voltage was doubled. 6 GES101 online SC Fall2020

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3. Keep resistance constant at values shown in the table and vary voltage to measure the current and fill your data in the table. Table 4. Measured current for varying voltages # Resistance (ohms) Voltage (v) I (mA) 1 200 2 10 2 200 4 20 3 200 6 30 4 200 8 40 5 400 2 5 6 400 4 10 7 400 6 15 8 400 8 20 Q4. Observe the trend in your data. a) When the voltage is doubled, how does the current change? (Does the current halve, double, triple….) - when the voltage doubles, the current also doubles. b) When the voltage triples, how does the current change? - if the voltage triples the current also triples. Q5. Why is the current in #2 and in #6 not the same? (V= 4 V in both cases) - they have different resistances which affects the current. 7 GES101 online SC Fall2020