Question

Q1

A potential difference of 13 V is found to produce a current of 0.45 A in a 3.1 m length of wire with a uniform radius of 0.36 cm. Find the following values for the wire: (a) the resistance (b) the resistivity

Answer 1

a).

resistance is equal to potential difference divided by current: R= V / I
so R= (13 Volts) / (.45 Amperes) = 28.89 Ohms

b). resistance is also equal to resistivity (symbol that looks like a "p") multiplied by length L divided by cross-sectional area A:
R= pL / A
so resistivity= p = RA / L
R= 28.89 Ohms
A= pi x radius^2 = pi (.0036 meters)^2 = 4.07x10^-5 meters squared
L= 3.1 meters
so, resistivity= (28.89)( 4.07*10^-5) / (3.1) = 3.79x10^-4
the unit is the ohm-meter

2)

the resistance of a wire is given by

R= pho L/A

R=resistance
rho = resistivity
L=length
A=area

the best way to approach this is to take the ratio of resistances, using "1" for Tungsten values and "2" for gold:

R1/R2= rho 1 L1/A1 / (rho 2 L2/A2)= (rho1/rho2)(A2/A1)

looking up values on line, the resisitivity of tungsten is 5.28x10^-8 ohm -meters, and gold's is 2.44x10^-8 ohm-m

since rho tungsten = 2.16 rho gold...then the A of the gold wire must be 2.16 times the area of the tungsten wire...since area goes as radius^2, the radius of the gold wire must be sqrt[2.16] times the radius of the tungsten wire, or 1.47 times greater