How much work W is done by the voltage source by the time the steady state is reached ? Express your answer in terms any or all of &, R, and C. ew Available Hint(s) W = Submit Now that we have a feel for the state of the circuit in its steady state, let us obtain expressions for the charge of the capacitor and the current in the resistor as functions of time, We start with the loop rule: & - VR - Vo = 0. Note that VR(t) = I(t) R. Vc(t) = 20, and I(t) = dal. Using these equations, we obtain do = - , and then, do(t) Q(t) CE=- Part H do(t) Integrate both sides of the equation )_co - RC to obtain an expression for q (t). Express your answer in terms of any or all of E, R, t, and C. Enter exp (x) for et. View Available Hint(s) 9 (t) = Submit Part I Now dit entiate q (t) to obtain an expression for the current I (t). Express your answer in terms of any or all of E, R. t, and C. Enter exp (X) for e. I (t) = Submit Request Answer Part J Find the time to that it would take the charge of the capacitor to reach 99.99% of its maximum value given that R = 12.0$2 and C = 500 /F. Express your answer numerically in seconds. Use three significant figures in your answer. View Available Hint(s) a = Submit Let us now consider a different R-C circuit. This time, the capacitor is initially charged (q(0) = q0), and there is no source of EMF in the circuit. (Figure. 2)We wil assume that the top plate of the capacitor initialy holds positive charge. For this circuit, Kirchhoff's loop rule gives I R + = 0, or equivalently. IR = -