Question

300-volt power station is connected to a factory through two power lines. If the factory is 5 Km away from the station and electric potential difference at factory 220 V, current intensity 100 A, calculate: a) The resistance of unit length. b) Radius of CSA of the wire. given that its resistivity 1.5x10-8 2.m.

Answer 1

The potential drop on the power line is equal

$$\Delta V=300\:\rm V-220\: V=80\: V$$

Hence, the resistance of the power line

$$R=\frac{\Delta V}{I}=\frac{80\:\rm V}{100\:\rm A}=0.8\:\Omega$$

a) The resistance of unit length

$$R/l=0.8\:\Omega/(2*5000\:\rm m)=8*10^{-5}\:\Omega/m$$

b) Radius of CSA of the wire

$$r=\sqrt{\frac{A}{\pi}}=\sqrt{\frac{\rho l/R}{\pi}}\\ =\sqrt{\frac{1.5*10^{-8}\:\Omega\cdot\rm m}{3.14*8*10^{-5}\:\rm\Omega/m}}=7.7*10^{-3}\:\rm m=7.7\: mm$$