The hotplate is connected to a 60 V network using wires that have some resistance. In this case, the voltage on the tile

The hotplate is connected to a 60 V network using wires that have some resistance. In this case, the voltage on the tile is 40 V. What will the voltage on the tile equal if the same tile is connected in series to it?

Let us denote the resistance of the wires by the letter r, and the resistance of the tile by the letter R. Since the current in the first circuit will be the same both in the tile and in the wires, the expression will be true:

20 / r = 40 / R.

Where from:

r = (20 x R) / 40;

r = 0.5 x R.

When another exactly the same tile is connected to this circuit, their resistances add up and the total resistance of the new circuit will be equal to:

r + R + R = 0.5 x R + R + R = 2.5 x R.

Now it is easy to calculate what voltage will be on the tile in the new circuit:

(60 / (2.5 x R)) x R = 24 (volts).

Answer: the voltage on the tile will be 24 volts.