A large power plant generates electricity at 120 kv its old...

A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 400 kV. The secondary of this transformer is being replaced so that its output can be 500 kV for more efficient cross-country transmission on upgraded transmission lines. (a) What is the ratio of turns in the new secondary compared with turns in the old secondary? (b) What is the ratio of new current output to old output (at 400 kV) for the same power? (c) If the upgraded transmission lines have the same resistance, what is the ratio of new line power loss to old?

Transcript

00:02 Dear students, let's denote the windings at the primary end is np and let's denote the windings at the secondary end with ns.

00:14 And we know that the relationship between number of tons of the coil to the voltage is equal to number of tons, the primary divided by voltage at the secondary.

00:27 So the ratio of the tons at primary and secondary is equal to the ratio.

00:31 Of the voltage is that primary and secondary so this is the relationship now simply plug in the values the voltage at the primary is given this is 12 kilowatts and the voltage at the secondary is given there is 400 kilo volts so from here we get the values of that is equal to 12 divided by 400 because this kilo volt and kilowalt cancels out so the ratio of primary and secondary comes out to be 12 divided by 4 -hundred now the windings at the secondary end has been changed let's say that has been changed from ns to let's say ns prime the new turns or the new one the new number of turns in the secondary are ns prime so let's use the equation again now the voltage at the primary and the turns at the primary divided by the turns at the secondary the new turns because at primary we have the same number of tons that would simply be equal to primary voltage divide by secondary voltage primary voltage is given it is not it is unchanged that is 12 kilowatts and secondary voltage has been changed just because of we have changed the secondary wind that is 500 kilo volts so this is equal to this kilo volt delay kilowalt cancels out so this is equal to 12 divided by 500 i guess so far so good.

01:59 Now we have to take the ratio.

02:02 All right.

02:03 Now let's denote this with equation number one and let's denote this with equation number two.

02:09 If we divide equation number one and equation number two, so that would simply be equal to by ns prime divided by np, this equation divides with the reciprocal of this equation.

02:23 There is ns divided by np.

02:27 So n s prime divided by np is 500 divided by 12 divided by ns divided by n s divided by np is 400 divided by 12 all right now this 12th and 12th cancels out 500 divided by 400 this will give us now here one more thing because this p np and p np cancels out this 12th and 12th cancels out so the new result is the number of tons at the secondary new tons to the number of tons at the secondary old is equal to all right 500 divided by 400 is 1 .25 so this is the ratio of the new tons to the old tons so this was part number a i hope you understood this now let's move to part number b here we have to do the same but with the currents you know that the current at the primary winding divided by the current at the secondary winding is equal to the voltage at the secondary divided by voltage at the primary...

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