# There are m resistor each of resistance R. First they all are connected in series and equivalent resistance is X. Now they are connected in parallel and equivalent resistance is Y.? What is the ratio of X and Y?

$Whenconnectedinseries\phantom{\rule{0ex}{0ex}}{R}_{eq}=R+R+.....+mtimes=mR\phantom{\rule{0ex}{0ex}}X=mR\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Whenconnectedinparallel\phantom{\rule{0ex}{0ex}}\frac{1}{{R}_{eq}}=\frac{1}{R}+\frac{1}{R}+.....+mtimes=\frac{m}{R}\phantom{\rule{0ex}{0ex}}So\phantom{\rule{0ex}{0ex}}\frac{1}{{R}_{eq}}=\frac{1}{Y}=\frac{m}{R}\phantom{\rule{0ex}{0ex}}Y=\frac{R}{m}\phantom{\rule{0ex}{0ex}}So\phantom{\rule{0ex}{0ex}}\frac{X}{Y}=\frac{mR}{\frac{R}{m}}={m}^{2}\phantom{\rule{0ex}{0ex}}$

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