The graph below shows the data of the resistance, R, across a wire versus the le

Question

The graph below shows the data of the resistance, R, across a wire versus the length, L, of the wire. The radius of the wire is 0.0765 mm and its end to end resistance is 47.85 ohm. Use proper graphical methods to calculate the slope for the graph below, What are the cross - sectional area and resistivity of the wire? What is the end to end length of the wire student used in this experiment? A 410.35 mm long wire made of same material and having the same diameter has a voltage of 4.15 volts applied across it. What current exists in the wire? Please show detailed calculation for each part of the question and use SI units.

Explanation / Answer

a) the first point coordinates are (0.08,4.000)

second point coordinates are (0.24,8.000)

slope is m = (y2-y1)/(x2-x1) = (8-4)/(0.24-0.08)= 25 ohm/m

b) cross sectional area is A = pi*r^2 = 3.142*(0.0765*10^-3)^2 = 1.84*10^-8 m^2

resistivity is rho = R*A/L = 8*1.84*10^-8/(0.24) = 6.13*10^-7 ohm-m

C) R1/L1 = R2/L2

8/0.24 = 47.85/L2

L2 = 1.4355 m

D) current i = V/R

R = rho*L/A = 6.13*10^-7*410.35*10^-3/(1.84*10^-8) = 13.67 ohm

i = V/R = 4.15/13.67 = 0.303 A

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