Further understanding Ohms Law

Question

I posted a question earlier that helped me to understand Ohm's Law and how power is lost to length of wire due to resistance. So my original example was a 15A, 10ft cable surge protector plugged into a 15A 6 foot cable plugged into a extension cord 13A 10ft which then has the appliance's cable at 8 ft. The max power this device would need is 110 watts.

We worked out Ohms law: 𝑃=0.922𝐴×0.434Ω=0.367𝑊

I do not understand how the 0.367 W applies to the power needed (110 watts)? Does this mean if the TV needs to pull at max and requests 110 watts it will only receive 109.64? This is safe and will it not damage any of the TVs components, I heard under powering is very bad.

Answer 1

Most appliances have regulated power supplies, meaning that they adjust the resistance they present to the power cable to ensure that they always get the same power.

However for devices without regulation, the device really will get less power. For example, people often expect to be able to string large numbers of 5v LED strips together, only to find that the further diodes get dimmer and eventually stop lighting up all together. This is due to the resistance of the wiring limiting how much power the more distant lights get.

Answer 2

The TV is not a resistor so Ohm's law does not apply to it. It has a switch mode power supply so it will try to pull the power it needs, regardless of wiring resistance.

Answer 3

To some degree you are overthinking this problem.

Let's start with your original problem: what is the effect of multiple extension cords on a 120 VAC television which needs 110 watts.

If you assume that the television was actually drawing 110 watts, then the power dissipated in the extension cords was calculated to be .376 watts. How much voltage is this ? Well, it's .92 x .434 (since Ohm's law says that voltage is current times resistance), or.399 volts. To put it another way, you'll only get exactly 110 watts if the line voltage at the wall plug is 120 + .399, or 120.399 volts.

Is this an issue?

Well, no. I suggest you look at this site for an idea of what you can actually expect from a power line at your house. The short version is that Range A, 114 to 126 volts, is what you can reasonably expect. Also note Range B, which suggests that, for limited periods of time, Range B is acceptable, and this indicates that you can actually expect your house voltage to vary between 110 and 127 volts, although the upper and lower limits should not occur often.

Your TV manufacturer is (or should be) aware of this, and have designed the TV accordingly. For that matter, the manufacturer would be well-advised to do somewhat better, in order to avoid a bad reputation.

With a potential line voltage which varies by 12 volts, reducing that range by 0.4 volts simply isn't something which you should worry about. It's only about 3% of the variation which the TV already expects.

If, for some reason, this were to become a problem, you would have much bigger problems on your plate already, as your electricity provider would be experiencing major issues, and you would be experiencing brownouts on a regular basis.

Finally, as Justme has answered, your TV is not a resistor. Its power supply almost certainly adjusts its operation to accept voltages other than 120 volts exactly. As far as it is concerned, voltage drop (and power loss) in your extension cords is no different than a low voltage from the electric company, and it will do just fine.

What you do need to be aware of is that the power lost in the extension cords shows up as heat, and if you get the cords hot enough they can do nasty things like catch fire. Since your current is only about 1 amp, and all of your cords are 13 amps or better, you should have no worries at all.