An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 30 mm and 80 mm. the electric potential of the inner conductor with respect to the outer conductor is -466 v (k = 1/4πε 0 = 8.99 × 109 n · m2/c2). the average energy density of the capacitor is closest to\

Now that we have a feel for the state of the circuit in its steady state, let us obtain the expression for the current in the circuit as a function of time. note that we can use the loop rule (going around counterclockwise): e−vr−vl=0. note as well that vr=ir and vl=ldidt. using these equations, we can get, after some rearranging of the variables and making the subsitution x=er−i, dxx=−rldt. integrating both sides of this equation yields x=x0e−rt/l. use this last expression to obtain an expression for i(t). remember that x=er−i and that i0=i(0)=0. express your answer in terms of e, r, and l. you may or may not need all these variables. use the notation exp(x) for ex.