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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