Answer:
Resistance = 68.23 Ω
Explanation:
Let's start off by remembering the fact that when resistors are connected in series, their resistances is added up to find the total resistance.
The equation for resistance using resistivity is given below:
Resistance = Resistivity * Length / Area
where Length = x
Resistivity = 3x^5
and Area = [tex]\pi *0.00016^2[/tex] = 8.04 * 10^(-8) meter squared
Substituting in the value of resistivity, length and area we get:
Resistance = [tex]\frac{ (3x^5) * (x) }{(8.04*10^-^8)}[/tex]
Resistance = [tex]\frac{ (3x^6) }{(8.04*10^-^8)}[/tex]
Since resistance in series is added, we can simply integrate this formula over the length (x = 0 to x = 0.2) to get the total resistance.
Resistance = [tex]\int\ {\frac{ (3x^6) }{(8.04*10^-^8)}} \, dx[/tex]
Resistance = [tex](5.4857*10^-^6) /(8.04*10^-^8)[/tex]
Resistance = 68.23 Ω
