a) If the capacitors C in the above problem areall replaced by identical resisto

Question

a) If the capacitors C in the above problem areall replaced by identical resistors R, what will be theeffective resistance of the configuration? b )If a potential difference VAB is appliedbetween points A and B, what will be thepotential
differences across the individual resistors in the top, middle andbottom rows? c)What will be the ratios of thecurrents in the middle and bottom rows compared to that in the toprow? (Answers: a)Rab = 6R/11; Top: VR = Vab. b)Middle: VR = Vab/2; Bottom: VR = Vab/3. c)Imiddle/Itop = 1/2;Ibottom/Itop = 1/3.

Explanation / Answer

If C are replaced by R In each row R are in series, they add up:    Rtop = R    Rmiddle = 2R     Rbottom = 3R Each row of resistora are in parallel. 1/Reff = 1/R + 1/2R + 1/ 3R            =(6 +3 + 2)/6R = 11/6R Reff = (6/11)R (b) Pot difference, Vtop =VAB                                  Vmiddle = VAB/2 across each resistor.                            Vbottom = VAB/3 across each resistor. (c) Itop = V?R = VAB/R      Imiddle =VAB/2R     Ibottom =VAB/3R Ratio,               Im/It = 1/2                Ib/Tt = 1/3

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