Asked by rick
A generating station is producing 1.3*10^6 W of power that is to be sent to a small town located 7.0 km away. Each of the two wires that comprise the transmission line has a resistance per kilometer of length of 5.0*10^-2 /km.
(a) Find the power lost in heating the wires if the power is transmitted at 1100 V.
(b) A 140:1 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires?
(a) Find the power lost in heating the wires if the power is transmitted at 1100 V.
(b) A 140:1 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires?
Answers
Answered by
Damon
power = voltage * current
P = V * i
1.3*10^6 = 1.100 *10^3 i
i = (1.3/1.1) * 10^3 = 1.182 * 10^3 amps (heavens!)
R = 14 km * 5*10^-2 ohms
R = 7 * 10^-1 ohms
Power lost = V i = (i R) i = i^2 R = 9.777 *10^5 watts (most of our power lost in transmission :( )
b. Mr Westinghouse told Mr. Edison to use AC so he could step up the voltage and lose less.
V = 140 * 1100 = 1.54 * 10^5 volts
(now we are talking)
i = 1.3*10^6 / 1.54 * 10^5
i = 8.44 amps
power lost = i^2 R = 8.44^2 (.7) = more like 50 Watts. Half a light bulb - Alright!
P = V * i
1.3*10^6 = 1.100 *10^3 i
i = (1.3/1.1) * 10^3 = 1.182 * 10^3 amps (heavens!)
R = 14 km * 5*10^-2 ohms
R = 7 * 10^-1 ohms
Power lost = V i = (i R) i = i^2 R = 9.777 *10^5 watts (most of our power lost in transmission :( )
b. Mr Westinghouse told Mr. Edison to use AC so he could step up the voltage and lose less.
V = 140 * 1100 = 1.54 * 10^5 volts
(now we are talking)
i = 1.3*10^6 / 1.54 * 10^5
i = 8.44 amps
power lost = i^2 R = 8.44^2 (.7) = more like 50 Watts. Half a light bulb - Alright!
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