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I know that at home the electric circuits are parallel, and this explains why if one appliance (eg bulb) fails, everything else continues to work, but if more devices are added in parallel to each other, their combined resistance should decrease, and thus the total power supplied by them should increase, as $\mathrm{Power} = V^2/ R$. It doesn't look like that's the case, what am I getting wrong?

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  • $\begingroup$ Let us continue this discussion in chat. $\endgroup$ – Harshit Joshi Sep 29 '18 at 14:25
  • $\begingroup$ Appliances don't 'supply' power (your wallet does that). $\endgroup$ – amI Sep 29 '18 at 16:18
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    $\begingroup$ Perhaps your problem is a linguistic one. You seem to be confusing the physics definition of power with the everyday English one used in e.g. "power company". If you think of your appliances as consuming energy rather than power, the question might answer itself. $\endgroup$ – jamesqf Sep 29 '18 at 17:11
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To minimize your power consumption and save on electricity bills, you actually want to maximize your home's equivalent resistance, for the reason you mention. This is done when every appliance is turned off, because each turned-off appliance has (approximately) infinite resistance (up to some current leakage). Adding a new turned turned-off appliance doesn't really create a new current path or decrease the equivalent resistance. Every time you turn on an appliance, you are closing a new circuit and decreasing your home's equivalent resistance, therefore increasing your power consumption.

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The power will increase .See the formula given carefully $V^2/R$. For constant voltage power is inversly propotional to resistance.As we add one more resistance in parallel overall resistance decreases and hence power increases.Or you can also think in the way if overall resistance decreases then current increases and hence $P=VI$ increases

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