Question

Resistance of a conductor of length $5cm$ in $4ohms$.If a cross-section area of the conductor is $0.5m{m}^2$, what is the specific resistance of the conductor?

Answer 1

Step1:- Given data

Resistance is $R=4\Omega$

length of conductor $l=5cm$

cross-section area $A=0.5m{m}^2$

Note:- $$\begin{gathered} \left(1meter=100cm \\ 1meter=1000mm\right) \end{gathered}$$

Step2:- Finding specific resistance.

We know that $R=\rho \frac{l}{A}$

Here $\rho =$specific resistance of the conductor.

Then,

$$\begin{gathered} \rho =\frac{RA}{l} \\ =\frac{4\times 0.5\times {10}^{-6}}{5\times {10}^{-2}} \\ =4\times {10}^{-5}ohm\times m \end{gathered}$$

Hence, the specific resistance of the conductor is $4\times {10}^{-5}ohm\times m$.