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 0.0685 mm and its end to end resistance is 43.65 ohm. (a) Use proper graphical methods to calculate the slope for the graph below. (b) What are the cross sectional area and resistivity of the wire? (c) What is the end to end length of the wire student used in this experiment? (d) A 450.35 mm long wire made of same material and having the same diameter has a voltage of 3.15 volts applied across it. What current exists in the wire? Please use SI units

Explanation / Answer

1. Slope of the graph = (y2-y1/x2-x1) = (33-3) / (0.94-0.08) = 34.88 ohms/m

2.Cross sectional area = Pi*r^2 = 3.14*0.0685^2 *10^-6 = 1.473*10^-8 m^2

3. Resistivity, Rho = R*A/L = (R/L)* Area = slope *area = 34.88 * 1.473*10^-8 = 51.39*10^-8 Ohm m

4. End to end Length of wire = L = R*A/Rho = 43.65*1.473*10^-8 / 51.39*10^-8 = 1.251 m

5. Current = V/R , Resistivity remains the same since the material for both wires is the same

Resistance for new wire = R = Rho * L /A = 51.39*10^-8 *0.45035/ 1.473*10^-8 = 15.69 Ohms

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