Hi, I am reading the textbook about DC circuits from this page. Its awesome but I think i found some nonsence. (I also think this was discussed here on this forum but I havent found it).
So, to the problem.
I am currenty on 7.4 chapter - COMPONENT FAILURE ANALYSIS
The textbook shows there example of 4 resistors connected like this : (R1//R2)--(R3//R4). We are solving what happens when R2 fails.
So the total resistance of R3//R4 is same as they are working as before. Trouble is that when R2 burns we have only R1. The textbook says that the total resistance of R1//R2 is lower after R2 burns. But I think its not true. Cos when 2 resistors are in parallel the total resistance is lower than value of the lowest resistor.
And when 2 is turned off the total resistance raises, but the texbook says the opposite : R of (R1//R2) > R of (R1).

Am I right or I've missed something

(i've built this circuit on my breadboard and it works the way i said...)

 

Maybe when a very old carbon composition resistor burns it turns into charcoal that has a lower resistance than before. Whatever caused R2 to overheat will also cause R1 to overheat and become a low resistance. The pcb will also probably turn into charcoal (if it is cheap phenolic) and then will have a low resistance.

 

Hmm, yea, but, by burning i meant something like disconneting, disappearing, "turning off" not literaly burning...

 

A modern carbon film or metal film resistor has a helix of its resistive material. If it is overloaded then it burns open so it "disappears".

The book is probably wrong.

 

Well, you left out a critical item....

Here's a link to the chapter you're talking about:
http://www.allaboutcircuits.com/vol_1/chpt_7/4.html

The critical text:

Next, we need a failure scenario. Let's suppose that resistor R2 were to fail shorted.

Realistically, about the only way a "real-world" resistor would become shorted is if a blob of solder shorted across it, or something else shorted it out like a stray piece of wire. Resistors almost always fail by burning open.

But going along with the scenario, if R2 shorted out, then R1//R2 = 0; so the total resistance would be (R1//R2)--(R3//R4) = (R1//0)--(R3//R4) = 0--(R3//R4) = R3//R4; which is about as far as we can go with that as the values for R3 and R4 have not been defined.