The region between two concentric metal spherical shells (radius a and b, respectively) is filled with a weakly conducting material of conductivity o. assume the outer shell is electrically grounded, and a battery maintains a potential difference of v = v between the two shells. (in this problem, don't confuse conductivity, o, with surface charge density. also, ignore any dielectric properties of the weakly conducting material). (a) what total current, i, flows between the shells? also, what is the total resistance, r, of the weakly conducting material between the shells? (b) revisit griffiths section 2.5.4, and re-express your final answers (for i and r) in part a, in terms of the total capacitance, c, for this same arrangement of two concentric shells. c) now, suppose the battery maintaining (vi=v, between the concentric spheres is suddenly disconnected at t = 0. (at t=0, av between inner and outer spheres is thus vo, but there is no battery to maintain this) describe qualitatively what you expect happens over time. then, calculate the voltage, and the current that flows, between the two shells as a function of time, i. e., find v(t) and it). does your calculation agree with your qualitative prediction? (d) for the situation of part c, calculate the original total energy stored in the spherical capacitor (use griffiths eq. 2.55). by integrating power (= v*i), explicitly confirm that the heat delivered to the resistance is equal to the energy lost!