When a switch is closed in a circuit containing resistance R, an inductance L, and a battery that supplies a constant voltage E, the current I builds up by a rate described by the equation L(dI/dt) + RI = E (a) Find the current I as a function of time. (b) If you measured the current in the circuit after a very long time, what would you expect? (c) How long will it take for the circuit to reach one half of its final value? (d) Determine the current I if its initial value is I_0 = I(0) = E/R when the circuit is turned on.