Question:

Estimate the resistance of the $120$-$\textrm{V}_\textrm{rms}$ circuits in your house as seen by the power company, when

- everything electrical is unplugged, and
- two 75-W lightbulbs are on.

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

- Resistance appears infinite.
- $96 \Omega$

### Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. he power output of a device is the rms current that it draws, multiplied by the rms voltage across it. And we can solve this for*V rms*by dividing both sides by the rms current. And that gives

*V rms*is power divided by rms current. But we don't know what this is, but we know that peak current instead. So we'll have to work with that. So, we know the peak -- or -- the rms current is peak current divided by root two. And so, we can substitute this in place of

*I rms*. So, when we divide by rms current, it's the same as multiplying by the reciprocal of the rms current. So we're gonna multiply by the reciprocal of this here, so which means flip it over. So we have,

*V rms*is gonna be

*P*times root two over

*I naught*, peak current. And, that's gonna be 1500 watts, times root two, divided by 6.4 amps, which is about 330 volts rms.