#### cepheid

Staff Emeritus

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The first is based on an observation. When we plug in our blow dryer, and turn it on, the lights dim noticeably. Why?

My attempt to think about it involved connecting another load in parallel with the lamps and seeing what happened to the current going through each of the lamps, assuming (in my model) that there were only two of them, and they were identical. If the current through each lamp was reduced, I would have my explanation. But how to model the blow dryer? I had no idea. But I noticed the ratings written on it: 1600 W, 125 VAC, 60 Hz (there was also an option to set it for 250 VAC and 50 Hz). Why 125 V? Isn't 120 V standard for N. America? No matter...in my model, to simplify things, I used unrealistic numbers. But I digress. Back to the problem of how to model the blow dryer. Since 1600 W was such a large number, and the blow dryer was visibly affecting the electricity available, I decided that it must be drawing a lot of current. So I modelled it as a resistor with very low resistance, compared to the two lamps. So here are my unrealistic numbers I used. Source: 10 V

2 Lamps: 10 ohms each. Blow dryer: 0.1 ohms.

current through each branch is the conductance, G_i, times the voltage, V_i, across the ith branch. V_i = V = 10 volts for all i, so the currents are:

I_1 = (10 V)(1/10) = 1 A

I_2 = I_1 = 1 A

I_3 = 10 X 10 = 100 A

By KCL, I_total = I_1 + I_2 + I_3

V X G_total = (V X G_1) + (V x G_2) + (V X G_3)

= V X (G_1 + G_2 + G_3) = 102 A, which was obvious from the very first line of equations, but I elaborated to show that conductances in parallel add together, since we're adding more conducting pathways to the circuit, and this is equivalent to saying that for resistances in parallel, the overall resistance is lowered i.e. instead of G's, it could have been written: 1/R total = 1/R1 + 1/R2 + 1/R3. We all know this.

The problem I'm having is that the current through each lamp is the same as it would be if the blow dryer were not connected in parallel with them, and it's never going to change. Even if the third load you connect in parallel with the two lamps has an even smaller resistance than 0.1 ohms, that will only change the *overall* current drawn by the circuit. Each branch still "sees" 10 V, so each of the lamps will still draw 1 amp. The blow dryer will simply be drawing more. That is my understanding. So why do the lights dim?

Of course I realise my model could be wrong. I'm assuming a blow dryer has a fan and some heating elements. If the heating elements are anything like those tungsten filaments in toasters or whatever, then they heat up and glow because they have *high* resistance, not low right? So maybe my model is bogus. I still don't see what difference it makes to the lamps though.

meh, this post is already much longer than I thought it would be, so I will wait for your insights on my first question, and come back to ask the second later.