PLEASE HELP!... Very confused on how to solve this problem. If you could please

Question

PLEASE HELP!... Very confused on how to solve this problem. If you could please show all of your work along with the answers that would be fantastic so I can understand it. Thank You!

The circuit shown below has been sitting with switch A open for a very long time. The resistors(green), the currents (red arrows), EMF(Orange) and capacitors(blue) are shown. The capacitance of a capacitor(blue) and the variable for its charge are listed together. When they flow, the currents flow in the directions shown 6R IB 3R 13C,Q3 ID 2R

Explanation / Answer

given initially the switch is open, when the swiotch is closed after a few milliseconds t

1. from kirchoff's loop equations for the loops in the diagram

form the outer loop

E = Ia*6R + Ib*4R

from the left side of outer loop and inner loop

E = Ia*6R + Q2/2C + Q1/C + 2R*Ic

here Q2 = Q1 = dIe/dt

form the right side of the outer and inner loops

Ib(4R) - Ic(2R) - Q3/3C = 0

from the inenr loop

Q2/2C + Q1/C = Q3/3C

Q2/2 + Q1 = Q3/3

as Q1 = Q2 = Q

3Q/2 = Q3/3

Q3 = 9Q/2

2. from kirchoff's junction rule

Ia = Ib + Ic

Ic = Ie + Id

3. for the given infinite circuit

let effective resistance be Reff

removing the forst 2R and R resistors will again give Reff

then

R and Reff are in series

and these both are in parallel to 2R

hence

Reff = 2R*(R + Reff)/(2R + R + Reff) = 2R(R + Reff)/(3R + Reff)

Reff^2 + 3R*Reff = 2R^2 + 2R*Reff

Reff^2 + R*Reff - 2R^2 = 0

solving for Reff

Reff = (-R + sqroot(R^2 + 8R^2))/2 = R

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