# 3 calculate the resistivity of the wire as a product

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Chapter 10 / Exercise 2
Delmar's Standard Textbook of Electricity
Herman
Expert Verified
3. Calculate the resistivity of the wire as a product of the slope times the area of the wire cross- section (Eq. 5): 𝜌 = ( 𝑆𝑙𝑜𝑝𝑒 ) × ( 𝐴𝑟𝑒𝑎 ) (5) 4. Compare the values of resistivity obtained in Parts I and II. Calculate average of these two values and percentage difference between them. Compare the value of resistivity you have measured with the known resistivities of different metals (see Table of Resistivities below) and identify the material the wire is made of. Table 1. Resistivity of Some Common Materials MATERIAL RESISTIVITY, ρ (Ω·m) Copper 1.72 x 10 -8 Aluminum 2.82 x 10 -8 Tungsten 5.60 x 10 -8 Steel 2.00 x 10 -7 Lead 2.20 x 10 -7 Nichrome (Ni, Fe, Cr alloy) 1.00 x 10 -6 Carbon (graphite) 3.50 x 10 -5 R L R I V Slope = = R L
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Chapter 10 / Exercise 2
Delmar's Standard Textbook of Electricity
Herman
Expert Verified
LAB WORK 3 Page | 18 PHY 156 Questions 1. What role does the ballast resistor R 0 play in the circuit used this lab work? 2. Based on the value of resistivity you calculated, what is the material the wire resistor is made of? 3. Is the wire resistor an ohmic conductor? Support your answer with the experimental data you obtained. 4. Do resistance and resistivity depend on: - the wire length? - the wire cross-section? - the wire shape?
PHY 156 Page | 19 LAB WORK 4 RESISTORS AND CAPACITORS CONNECTED IN SERIES AND IN PARALLEL Objective Task 1: To measure total resistance of resistors connected in series and in parallel and compare the measured values with the calculated ones. Task 2: To measure total capacitance of capacitors connected in series and in parallel and compare the measured values with the calculated ones. Physical Principles It is known that the total resistance R T of n resistors connected in series (Fig. 1a) equals sum of their resistances (Eq. 1): 𝑅 𝑇 = 𝑅 1 + 𝑅 2 + 𝑅 3 + + 𝑅 𝑛 (1) Fig. 1. (a) Circuit of resistors connected series. (b) Circuit of resistors connected in parallel. If the resistors are connected in parallel (Fig. 1b), their total resistance R T can be found using the following formula (Eq. 2): 1 𝑅 𝑇 = 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3 + + 1 𝑅 𝑛 (2) Total capacitance C T of n capacitors connected in series (Fig. 2a) and in parallel (Fig. 2b) can be found in a similar way. However, the formulae (1) and (2) must be swapped. That is, the total capacitance of capacitors connected in series is given by the formula (Eq. 3): 1 𝐶 𝑇 = 1 𝐶 1 + 1 𝐶 2 + 1 𝐶 3 + + 1 𝐶 𝑛 , (3) whereas the total capacitance C T of capacitors connected in parallel is just a sum of the involved capacitances (Eq. 4): 𝐶 𝑇 = 𝐶 1 + 𝐶 2 + 𝐶 3 + + 𝐶 𝑛 (4) R 1 R 2 R n R 1 R 2 R n ..... (a) (b)
LAB WORK 4 Page | 20 PHY 156 Fig. 2. (a) Circuit of capacitors connected in series. (b) Circuit of capacitors connected in parallel. Real circuits of resistors and capacitors may have various combinations of series and parallel connections. The simplest combinations can be explored using only three resistors, or three capacitors. The formula for total resistance of three resistors in series (Fig. 3a) is simplified to (Eq. 5): 𝑅 𝑇 = 𝑅 1 + 𝑅 2 + 𝑅 3 (5) and for three resistors in parallel (Fig. 3b) we have (Eq. 6): 𝑅 𝑇 = 𝑅 1 𝑅 2 𝑅 3 𝑅 1 𝑅 2 + 𝑅 2 𝑅 3 + 𝑅 1 𝑅 3 (6) Fig. 3. (a) Circuit of three resistors connected series. (b) Circuit of three resistors connected in parallel.