Transformers and the power grid.

Step 1 of 6

The turns ratio

A transformer is two coils wound on the same iron core, with no electrical connection between them. Alternating current enters the primary coil, which is connected to the generator. It makes a flux in the core that rises, falls and reverses, and that changing flux passes through the secondary coil too and induces a voltage in it, by Faraday’s law from the last Lesson.

The same flux passes through every turn of both coils, so every turn gets the same voltage. Each coil’s voltage grows with its number of turns:

$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$\frac{V_s}{V_p} =$$\frac{N_s}{N_p}$⁠

In the Scene, the power station’s generator makes 25 kV, and the transformer beside it feeds a 100 km power line to a town. Right now the Turns ratio is $1$⁠: both coils have the same number of turns.

Step 2 of 6

The current comes down

The tags above the Scene show the voltage and current on each side of the transformer. A transformer adds no energy, and a good one hardly loses any, so the power in equals the power out:

$V_p I_p = V_s I_s$⁠

If the voltage goes up 16 times, the current must come down 16 times.

Step 3 of 6

The same power

Now the Turns ratio is $16$⁠, and the line runs at 400 kV. Show current and losses is On: the transformer’s tank is see-through, and each limb of the core has a few thick turns on the station side and 16 times as many thin turns on the line side. Compare the two tags.

Step 4 of 6

Alternating current only

Everything a transformer does goes through a changing flux in the core. That is why the grid runs on alternating current, which reverses 50 times a second.

Step 5 of 6

Heat in the line

Each wire of the line has resistance, and the current turns $I^2 R$⁠ of power into heat in it. For the same power $P$⁠ sent, a high voltage means a small current, and working out the loss in the line’s three wires gives

$P_L = \frac{P^2 R}{V^2}$$P_L =$$\frac{P^2 R}{V^2}$⁠

where $R$⁠ is each wire’s resistance and $V$⁠ the line’s voltage. The line now runs at 100 kV.

Step 6 of 6

Double the voltage

$V$⁠ appears in the formula squared, in the denominator. Predict what will happen to the heat when the voltage doubles, then choose On under Show current and losses and look at the chart.

Try it: after predicting, slide Turns ratio from 1, no step-up at 25 kV, to 2, 4 and 16: 50 kV, 100 kV and 400 kV, and watch the wires cool and the town light up. That is why power lines run at hundreds of thousands of volts, and step-down transformers bring the voltage back to 230 V before it reaches a home.

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