I know it looks long but it only ask for expressions that's all. please help me

(4%) Problem 24: Discharging a Capacitor: An RC circuit includes a basic switch. In position "a", the battery, resistor and capacitor are connected in series, and the capacitor charges. In position "b" , the battery is replaced with a short, and the capacitor will discharge. Two voltmeters and an ammeter have been added to the circuit. $8 10% Part (a) With the capacitor being charged to some degree, the switch is moved to position "b" , and the capacitor begins discharging. At any given instant in the process, let I represent the current owing through the arnrneter, and let q represent the charge that remains on the positively charged capacitor plate. Enter an expression for Kirchhost Loop Rule where the sum of the voltage changes totals zero. 0 = R + a/C v0 x 83 10% Part (b) Since current is the rate of charge ow, substitute dq f r dt 0 I in your expression from the previous step. With a little algebra, rearrange your expression so that all references to time appear on the left-hand side, and all references to charge appear on the right-hand side. Input an expression for the right-hand side of your equation that is equal to (it where r 7: = RC. (Henceforth we use a short-hand notation for the "time constant" and substitute 1' for the product RC.) d ' =-V0/R x 1' Q 10% Part (c) Assume that the capacitor has an initial charge qo when the switch is moved to position "b" at time to . Which of these equations is a correctly written integral expression including the correct limits? (Recall the shorthand notation for the time constant introduced in the previous step, 7: = RC.) Q 10% Part (d) Input an expression for the charge on the capacitor as a function of time. Q 10% Part (e) For the time period While the capacitor is discharging, what is the magnitude of the maximum value of the current? * 10% Part (f) Input an expression for the current as a function of time. You must write your expression in terms of max . I(t) = Umax! X Attempts Remain - * 10% Part (g) Enter an expression for the voltage measured across the resistor, VR , as a function of time. VR(1) = Voe t/t x Attempts Remain Feedback: is available. 4 10% Part (h) Enter an expression for the maximum voltage measured across the capacitor, Vmax , during the period of time starting with the switch being moved to position "b". 4 10% Part (i) Enter an expression for the voltage measured across the capacitor, Vc, as a function of time. Your expression must be in terms of the Vmax entered in the previous step