Question

Calculate the length of a constant wire of cross sectional areas 4π x 10^8m and resistivity 1.1 x 10^-6Ωm required to construct a standard resistor of resistance 21Ω (take π=22/7)

Answer 1

The resistance in terms of conductor length $L$, area $A$ , and resistivity $\rho$ is

$$R=\frac{\rho L}{A}\rightarrow \\ \space\\L=\frac{RA}{\rho}=\frac{21\cdot4π \cdot10^8 }{1.1 \cdot 10^{-6}}=2.4\cdot10^{16}\text{ m}.$$

Longer than the distance from the Sun to Saturn!