Many cheap electric stoves have three settings on their switch (besides OFF) lab

Question

Many cheap electric stoves have three settings on their switch (besides OFF) labelled LOW MED and HIGH. This is actually achieved by making the heating element with three resistive coils each of equal resistance R. The switchthe arranges these resistors i) in series ii) with two in parallel connected in series to the remaining one, and iii) all three in parallel.

a) Which combinationgives LOW, MED, and HIGH?

b) What is the total element resistance in each case?

c) If the high setting is 1000W what is the power of LOW and MED? Is it really a good set of values for LOW, MED, and HIGH?

Explanation / Answer

a) LOW when all in series....because all in series leads to high resistance,low current ,low heat...

similarly MED for two in parallel one in series
HIGH when all are in parallel

b) all series total resistance = 3R
two parallel one series = (R*R)/2R + R = 1.5R
all parallel = R/3

c) suppose V= net voltage

HIGH = V^2/(R/3) = 3v^2/R

LOW = V^2/(3R) = V^2/3R

MED = V^2/(1.5R) = 2V^2/3R

when HIGH = 1000W

LOW = 1000/9 = 111.11W

MED = 2000/9 = 222.22W

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