# Simple Circuit

#### anthony618

Joined Nov 10, 2011
3
Hi everyone,

I'm having trouble with this problem from my physics class. It seems like it should be really simple, but I can't seem to figure out where to go with it.

Consider the case of a toaster oven and a light bulb connected to the same household circuit. Such elements are connected in parallel. If there is significant contact resistance (R_c) in the common part of the circuit, then the light bulb will dim when the oven turns on.
Assume that one day you observe that the lamp in your room dims to approximately half of its original brightness when a toaster oven on the same circuit is turned on. Estimate the contact resistance.

I had to make some assumptions, so I assumed the light bulb had P = 60 W and the oven had P = 1200 W. I also know that since the brightness of the bulb is about half, then then power must be half too (I = P/A, A is constant). I wrote down some equations that I know should be true, but I'm not sure where to go next. If anyone could steer me into the right direction, it would be greatly appreciated!

#### Jony130

Joined Feb 17, 2009
5,183
When light bulb is dim to half of its brightness.
This means that voltage across the light bulb is equal to 55V.

#### #12

Joined Nov 30, 2010
18,210
I might be a lot slower than you, but I used P=IV and V=IR several times.
I also assumed 120 volts for the power line because it's almost easy enough to do the math in your head with that voltage.
I for the toaster then R for the toaster.
I for the light bulb, then R for the light bulb.
Figure the 2 resistances in parallel, and
assume that half the voltage is on the switch contacts. Then the resistance of the switch is the same as the paralleled resistances of the loads.

This neglects the change of resistance of the light bulb filament with temperature and the likely condition that the bulb dims to half brightness with most of the voltage still available. Is your schooling still so early that this kind of assumption might be acceptable, or are you supposed to know how to figure these things?

#### bountyhunter

Joined Sep 7, 2009
2,512
When light bulb is dim to half of its brightness.
This means that voltage across the light bulb is equal to 55V.
I don't think bulb brightness is linear with applied voltage. I think there is some non linearity (?)

Joined Dec 26, 2010
2,148
I don't think bulb brightness is linear with applied voltage. I think there is some non linearity (?)
It's pretty savage, actually. This page gives some graphs that suggest that a typical lamp falls to 50% brilliance at a bit over 80% of nominal voltage.

http://www.lamptech.co.uk/Documents/IN Voltage.htm

The question would be whether the OP would be expected to have such information. I would think it more likely that a fall to half power would be expected, with the lamp and oven modelled as fixed resistances. Otherwise the student would end up with non-linear equations, or messy graphical solutions.

#### anthony618

Joined Nov 10, 2011
3
Adjuster is right. I'm taking an elementary physics course so the circuits we're studying are pretty simple--the resistances should be fixed.

#### anthony618

Joined Nov 10, 2011
3
The problem I'm having now is trying to relate everything so that the only unknown I have is R_c, which is what I'm solving for. I can get the problem down to an equation for R_c involving E and the P's for the oven and the light, but there's also the voltage for the two appliances (which are the same because they are in parallel, correct?). Is there anyway to relate that voltage to E and/or the P's, since those are the only values I know?

#### crutschow

Joined Mar 14, 2008
25,465
Since we assume the voltage drops to 1/2 the supply due to contact resistance then how would the contact resistance compare to the toaster resistance? Think of two resistors in series. (You can basically ignore the bulb resistance since it is so much higher than the toaster resistance)