$1\, MW$ power is to be delivered from a power station to a town $10\, km$ away. One uses a pair of $Cu$ wires of radius $0.5\, cm$ for this purpose. Calculate the fraction of ohmic losses to power transmitted if
$(a)$ power is transmitted at $220\, V$. Comment on the feasibility of doing this.
$(b)$ a step-up transformer is used to boost the voltage to $11000\, V$,power is transmitted,then a step-down transformer is used to bring voltage to $220\, V$.
Given: $\rho_{Cu} = 1.7 \times 10^{-8}\, \Omega \cdot m$.

(B) Length of copper wire $L = 2 \times 10\, km = 20000\, m$. Resistance $R = \rho \frac{L}{A} = \frac{1.7 \times 10^{-8} \times 20000}{\pi \times (0.5 \times 10^{-2})^2} \approx 4.33\, \Omega$. Current $I = \frac{P}{V} = \frac{10^6}{220} \approx 4545.45\, A$. Power loss $P_{loss} = I^2 R = (4545.45)^2 \times 4.33 \approx 8.95 \times 10^7\, W$. Since $P_{loss} > P_{transmitted}$,this is not feasible.
$(b)$ New current $I' = \frac{P}{V'} = \frac{10^6}{11000} \approx 90.91\, A$. Power loss $P'_{loss} = (I')^2 R = (90.91)^2 \times 4.33 \approx 35785\, W$. Fraction of power loss $= \frac{35785}{10^6} \approx 0.0358$ or $3.58\%$.