# Two spirals with resistances of 100 ohms and 200 ohms were used to make an electric hot plate designed

Two spirals with resistances of 100 ohms and 200 ohms were used to make an electric hot plate designed for a voltage of 210 V. The power of the tile is changed by switching the spirals. Find the lowest possible tile power.

There are 4 options for switching on:
1) Only the first spiral;
2) Only the second spiral;
3) Two in series;
4) Two in parallel.

Let’s calculate the power for all options:
Power, at the first spiral:
P1 = U * I1 = U² / Rtot
Rtot = R1
P1 = 210² / 100 = 441 W.
Power, with the second spiral:
P2 = U * I2 = U² / Rtot
Rtot = R2
P1 = 210² / 200 = 220.5 W.
Power with serial connection of spirals:
P3 = U * I3 = U² / Rtot
Rtot = R1 + R2
P3 = 210² / (100 + 200) = 147 W.
Power with parallel connection of spirals:
P4 = U * I4 = U² / Rtot
Rtot = R1 * R2 / (R1 + R2)
P4 = 210² (100 + 200) / (100 * 200) = 662 W.

Answer: the minimum power of the coil is 147 watts.

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