Question

Find error in calculation of resistivity of R = 65 ? 1 O l = 5 ? 0.1 mm d = 10 ? 0.5 mm

• A. 0.13
• B. 0.21
• C. 0.16
• D. 0.41

Answer 1

Answer: (A)

0.13

Answer 2

$R=\frac{\rho l}{\pi\left(d / 2\right)^{2}} \Rightarrow R=\frac{4\rho l}{\pi d^{2}} \Rightarrow \rho=\frac{\pi Rd^{2}}{4l}$
$\frac{\Delta\rho}{\rho}=\frac{\Delta R}{R}+\frac{2\Delta d}{d}+\frac{\Delta l}{l}$
$\Rightarrow \frac{\Delta\rho}{\rho}=\frac{1}{65}+\frac{2.\left(0.5\right)}{10}+\frac{0.1}{5}$
$\Rightarrow \frac{\Delta\rho}{\rho}=0.015+0.1+0.02$
$\Rightarrow \frac{\Delta\rho}{\rho}\approx0.13$
So 13% error.