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

Dear Student,
Resistance of 40 W appliance be R1 and of 60 W appliance will be R2.
When connected in series, current through both the appliances is same. Let the common current be I.
Power, $P={I}^{2}R$

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