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Question

Physics Question on Current electricity

A resistor is constructed as hollow cylinder of dimensions ra=0.5 cm{{r}_{a}}=0.5\,cm and rb=1.0 cm{{r}_{b}}=1.0\,cm and ρ=3.5×10−5Ωm\rho =3.5\times {{10}^{-5}}\Omega m . The resistance of the configuration for the length of 5 cm cylinder is ... ×10−3Ω\times {{10}^{-3}}\Omega .

A

7.42

B

10.56

C

14.38

D

16.48

Answer

7.42

Explanation

Solution

Given: l=5 cm=5×10−2m,l=5\,cm=5\times {{10}^{-2}}m, ρ=3.5×10−5Ωm\rho =3.5\times {{10}^{-5}}\Omega m A=π(1×10−4−0.25×10−4)A=\pi (1\times {{10}^{-4}}-0.25\times {{10}^{-4}}) =0.75π×10−4m=0.75\pi \times {{10}^{-4}}m =7.5π×10−5m=7.5\pi \times {{10}^{-5}}m ∴\therefore R=ρlA=3.5×10−5×5×10−27.5π×10−5R=\frac{\rho l}{A}=\frac{3.5\times {{10}^{-5}}\times 5\times {{10}^{-2}}}{7.5\pi \times {{10}^{-5}}} =7.42×10−3Ω=7.42\times {{10}^{-3}}\Omega