Does a parallel circuit in household electricity decrease electricity bills, as the total voltage needed is less, so therefore, the total energy consumed is also less?

Expert Answers
pnrjulius eNotes educator| Certified Educator

Wiring in parallel would do absolutely nothing to affect your electricity consumption, and could actually be quite dangerous due to the wild swings in resistance that would occur as appliances are plugged and unplugged. Make sure your circuit breakers are in good shape!

The reason it wouldn't affect electricity consumption is quite simple: Appliances need a certain amount of energy to operate, so they consume that much energy. A 40-watt light bulb draws... 40 watts, regardless of how it is wired. Most appliances actually require a certain voltage anyway, so they have transformers built into their AC adapters that step the voltage down to what they use.

The reason it would be dangerous is a bit harder to see; it comes from the fact that resistance in series adds linearly (normal addition), but resistance in parallel adds harmonically (reciprocal of the sum of the reciprocal).

That is, if you have appliances with resistances R1, R2, and R3, and you wire them in series, you simply get:
`R = R_1 + R_2 + R_3`

But if you wire them in parallel, you get instead:
`R = 1/(1/R_1 + 1/R_2 + 1/R_3)`

The latter is much more unstable to adding or removing items. For example, suppose I have a 50-ohm refrigerator, a 10-ohm television, and a 1-ohm smartphone.

In series, when all three are plugged in the total resistance is 61 ohms.
`50 + 10 + 1 = 61`

When I unplug my smartphone, the total resistance is 60 ohms.
`50 + 10 = 60`

But in parallel, all three plugged in have a resistance of only 0.89 ohms:
`1/(1/50 + 1/10 + 1/1) = 0.89`

If I unplug my smartphone, suddenly the resistance shoots up to 8.3 ohms:
`1/(1/50 + 1/10) = 8.3`

The removal of the smartphone decreases series resistance by less than 2%; but it increases parallel resistance by 900%.