# Two appliances of power 40 W and 60W are connected in series and parallel respectively . Find which appliance has higher resistance in each case.

Resistance of 40 W appliance be R

_{1}and of 60 W appliance will be R

_{2}.

When connected in series, current through both the appliances is same. Let the common current be I.

Power, $P={I}^{2}R$

$So,R=\frac{P}{{I}^{2}}$

So,

${R}_{1}=\frac{40}{{I}^{2}}\phantom{\rule{0ex}{0ex}}{R}_{2}=\frac{60}{{I}^{2}}$

So, in series combination, 60 W appliance offers more resistance.

When connected in parallel, potential difference across the 40 W and 60 W appliances will be same. Let the potential be V.

Power,

$P=\frac{{V}^{2}}{R}\phantom{\rule{0ex}{0ex}}Thus,\phantom{\rule{0ex}{0ex}}R=\frac{{V}^{2}}{P}$

So,

${R}_{1}=\frac{{V}^{2}}{40}\phantom{\rule{0ex}{0ex}}{R}_{2}=\frac{{V}^{2}}{60}$

So, in parallel connection 40 W appliance show more resistance.

Regards

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