An electric power station ( 100 MW) transmits power to a distant load through long and thin cables. Which of the two modes of transmission would result in lessere power wastage : Power transmission of : (i) 20,000 V or (ii) 200 V?

Explanation

Let R be the resistance (in ohm) of transmission cables.
Power of electric station,
`P = 100 MW = 100 xx 10^(6) W`
`= 10^(8)W`
(i) `V_(1) = 20,000 V`,
Current `I_(1) = P/V_(1) = 10^(8)/20,000 = 5000 A`
Rate of heat dissipation at 20,000 V is
`P_(1) = I_(1)^(2) R = (5000)^(2)R`
`= 25 xx 10^(6)R watt`
(ii) `V_(2) = 200 V`,
current `I_(2) = P/V^(2) = 10^(8)/200 = 5 xx 10^(5)A`
Rate of heat dissipation at 200 V is
`P_(2) = I_(2)^(2)R = (5 xx 10^(5))^(2) xx R`
`= 25 xx 10^(10)R watt`
As `P_(1) lt P_(2)`, therefore, there will be lesser power wastage when the power is transmitted at 20,000 V.