First, let's calculate the specific resistance (rho) using the given parameters. We can do this using the following equation:
rho = πr²R / l.
Substitute the respective values of r=0.26cm, R=64 Ω and l=156cm into the formula to calculate rho:
rho = π * (0.26)^2 * 64 / 156. This gives rho as approximately 0.0871.
Next, to calculate the total uncertainty (delta_rho_upper) in rho, we will need to find the partial derivatives of rho with respect to each variable (r, l, R) first.
The partial derivative of rho with respect to r (drho_dr) is
2πrR / l = 2 * π * 0.26 * 64 / 156.
The partial derivative of rho with respect to l (drho_dl) is
-πr²R / l² = - (π * (0.26)^2 * 64) / (156)^2.
And the partial derivative of rho with respect to R (drho_dR) is
πr² / l = π * (0.26)^2 / 156.
After calculating these derivatives, we can then estimate the upper bound for the error in rho (delta_rho_upper).
This is given by:
delta_rho_upper = (|drho_dr| * delta_r) + (|drho_dl| * delta_l) + (|drho_dR| * delta_R),
where delta_r, delta_l, and delta_r are the given uncertainties of r, l, and R respectively. In this case, delta_r=0.02cm, delta_l=0.1cm, and delta_R=2Ω.
Performing the substitutions, we find that delta_rho_upper is approximately 0.0162.
Finally, we can find the percentage error (percent_error_upper) for rho. This is done by the formula:
percent_error_upper = 100 * delta_rho_upper / rho
By substituting for delta_rho_upper and rho, we find the percent_error_upper to be approximately 18.57%.
Hence, we have the following results:
rho=0.0871, delta_rho_upper=0.0162, and percent_error_upper=18.57%. Please note, all values are rounded to 4 decimal places.
So, we can say that the specific resistance is 0.0871 ohms.cm, with a maximum error of 0.0162 ohms.cm and a relative error % of 18.57%, within the acceptable range of uncertainties.