Quote (FamilyGuyViewer @ Apr 19 2013 04:51pm)
the re resistance of which lightbulbs?
hmm maybe adding E will decrease the birghtness of bulb A but it would have the same brightness as C and D because of pararel circuits. if this is the right explanation then idk how to put it in terms of the equations
I'm talking about the equivalent resistance of the circuit in general. If R,eq goes down then the total circuit current increases (I = V/R, assuming the emf is constant). Now that the current is increased it will make A brighter(P = I^2*R). Then the current will split between B and the CDE(which will split again across each light bulb) parallel connection. Since the total current has increased the current across B will increase making it brighter, but because the current is being split to CDE instead of just CD the 3 in parallel will become dimmer.
I'm not sure how understandable I've made this but this sounded much better on paper
as far as the equation
assuming each resistor is equal to R
Switch open
C and D in parallel
1/Rcd = 1/RC+1/RD = 2/R ---> Rcd = R/2
B and CD in parallel
1/Rp = 1/RB + 2/R [1/Rcd]= 3/R --> Rp = R/3
A and Parallel bulbs in Series
R + R/3 = 4R/3
Switch Closed
C D and E in parallel
1/Rcde = 1/RC + 1/RD + 1/RE = 3/R --> Rcde = R/3
B and CDE in parallel
1/Rp = 1/Rb + 3/R [aka 1/Rcde] = 4/R ---> Rp = R/4
A and parallel parts
R + R/4 = 5R/4
This post was edited by drxscillator on Apr 19 2013 04:22pm