a) Determine the equilibrium charge on the capacitor in thecircuit as a function

Question

a) Determine the equilibrium charge on the capacitor in thecircuit as a function of R. b) Evaluate the charge when R = 10.0.c) Can the charge on the capacitor be zero? If so, for what valueof R? d) What is the maximus possible magnitude of the charge onthe capacitor? For what value of R is it achieved? e) Is itexperimentally meaningful to take R = infinity? Explain youranswer. If so, what charge magnitude does it imply? suggestion: Youmay do part b) before part a) as practice for it. The way I have it set up is: the resistances are all in ohms and the capacitor is 3F. I1 splits off down the left side of the circuitwhere it hits resistance R1 and R2. I2 splits down the right sideof the circuit and hits R3 and R4.
I started of by doing part b like it said. I found I,I1,I2 bysaying that I1(R1+R2) = I2(R3+R4) and solving for both of them withthe equation I=I1+I2. I got I1 = 5/83 A and I2 = 5/12 A. I figuredsince the current finds the path of least resistance that therewouldn't be any current flowing from I2 which means theres onlycharge from I1 where it would all cross accross thecapacitor. I solved for Q by saying that V=IR = q/c. The Q that I found is 5.42x10-7. Am I doing this right? Also what exactly does it mean by theequilibrium charge on the capacitor in part a. Is that not the samething as the charge on the capacitor being 0?

Explanation / Answer

(a) the voltage on the left side of the cap is determined byvoltage division: 80 / (80 + 3) * 5V = 4.82 V similarly, the voltage on the right side is: R / (R + 2) * 5V not sure which side is the (+) side, so i'll make the right side(+). The voltage across the capacitor is: 5 * [ R / (R + 2) - 80/83 ] now, Q = CV Q = 15E-6 * [ R / (R + 2) - 80/83 ] (b) plug in 10 for R Q = -1.958 micro coulombs (c) yes, solve Q = 0 for R... 53.33 (d) max value would be for R = 0, and it is -14.46 microcoulombs (e) yes, R = is an open circuit, making the voltage on theright side 5V. Q would be +542 nano coulombs

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