A few solutions to the homework

First, lets start with the last one...
Similar to the one I worked out in the discussion on the previous post.

Total resistance: 10+ 3.333 = 13.333 ohms. This is because the three 10's in parallel give you an equivalent resistance of 10/3.
So, with the voltage of the circuit as 3V, and the resistance is 13.333 ohms, then the current is V/R = I = 3/13.333 = .225 amps.

That's the current through the first resistor, so V=IR gives us V=.225 * 10 = 2.25 Volts.
The current through the other resistors is same .225 amps, split three ways. So .225/3 = .075 amps.
The voltage drop across the other three is 3-2.25 = .75 V (the first resistor had a drop of 2.25, so only .75 was left for the rest. in parallel, each resistor gets the full voltage, so V=0.75 Volts.

The power output of the first resistor is P=IV = .225 * 2.25 = .506 watts
For each of the other three resistors, P=IV=.075 * .75 = .056 watts. So the total power output of the system is P=.506 + .056 + .056 + .056 = .675 watts


Now for the modern holiday lights.
each string of 5 lights has a total of 120V across them.
So the voltage drop across a single bulb is 120/5 = 24 V
if P=2.4W, then P=IV becomes 2.4=I*24, so I=0.1 amps
Since we have 10 of these in parallel, that's a total of 1 amp of current running out of the outlet.
The resistance for a single bulb can be found from V=IR, where V=24 for a single bulb, I=0.1 A running through a single bulb, and so R=V/I = 24/0.1 = 240 ohms.
Yes, this is a very different resistance from the old fashioned bulb.
If one burns out? Well, that set of 5 goes out, but the other 45 lights stay lit.

Most modern bulbs nowadays actually has an extra metal wire that is an even worse conductor than the filament, but is not easily broken, running across the posts inside each little bulb. If the filament breaks, then electricity goes through that other wire and the rest of the lights in the series still gets current.

Read through the older posts on the blog for helpful stuff on the rest of the homework and the quiz.

Good luck with the quiz tomorrow. :-)