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Question:

How come step-up transformers reduce current in transmission lines?

By applying ohms law in the secondary circuit, IV(stepped up)/R , a stepped up voltage would result in an increase of current, i am aware that the step up transformer steps down current, but it is the secondary circuit that determines the current draws (ohm's law), and the primary current is multiples of itSo ?!!!!

Answer:

E IR P (watts) I^2 R or E^2 / R there have to be TWO transformers. gererator medium V, I first step, up, Hi V low I, Transmission loss low; low I^2 x R line Second step, down V, Low (220 or 110) V; High I, 50 to 100 amp for house hold. high I on motors and lights, high heat loss. high I needed for motor torque. edison had DC, did not understand AC math DC required huge I in transmission lines and limited line lenght to a few miles at most. due to I^2 R loss. Without complex number math for AC Electrical calculations we would not have the same technology that we do have, or radio. Math is the queen of science, Nerds rule
Here are some basic equations for transformer. V-high / V-low N-high / N-low Eq. 1 I-low / I-high N-high / N-low Eq. 2 where, V-high voltage at high voltage side V-low voltage at low voltage side I-high current at high voltage side I-low current at low voltage side N-high number of winding turns at high side N-low number of winding turns at low side Eq. 2 above could be written as I-high (N-low / N-high)I-low substitute Eq. 1 I-high (V-low / V-high)I-low Eq. 3 Let us have an example to give a good answer to your question. Consider a 30 MVA, 13.8-138 kV, 3-phase step up transformer. The 13.8 kV is at the generator side and the 138 kV is at the transmission side. Low side current is I-low 30,000,000 / 1.732(13,800) 1255 A High side current is I-high 30,000,000 / 1.732(138,000) 125.5 A it shows that I-high is less than I-low. Also, using Eq. 3 to further confirm result, we have I-high (V-low / V-high)I-low I-high (13,800 / 138,000) 1,255 I-high 125.5 A
I can't make too much sense out of your question. Your use of Ohm's law implies a constant resistance, which is not true. Power is constant between the input of a transformer and the output. When you increase the voltage you decrease the current, and the power remains constant (with a small lose due to inefficiencies). .
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Transformer coils are electrically isolated, the voltage in the secondary being induced by that in the primary. There is therefore no constant current between. The POWER (WAV) in the primary has to have an an induced equal counterpart in the secondary. In this case, as the voltage in the secondary is larger, the current drops proportionally. At the end of the transmission line it's stepped down again, and then you get a current.

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