[8%) Problem 11: Discharging a Capacitor: An RC circuit includes a bastc swrtch. In posrtion \"a", the 3attery._ 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 '0 the circuit 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 n the process, let I represent the current flowing through the annneter, and let q represent the charge that remains on the positively charged capacitor plate Enter an expression for Kirchho's Loop Rule where the sum of the voltage changes totals zero. Grad 100% Correct Answer Student Final Submission Feedback 0 = ,1 R , q 'C 0 = qs'C , I R Correct! Grade Summary dt 10% Part (b) Since current is the rate of charge flow, substitute - for I in your expression from the previous step. With a little algebra, rearrange your cession 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 of your equation that is equal to - dt where T = RC. (Henceforth we use a short-hand notation for the "time constant" and substitute T for the product RC.) dt T = dq/q V Correct! 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 ten integral expression including the correct limits? (Recall the shorthand notation for the time constant introduced in the previous step,T = RC!)_ da Correct!J Correct! $3 10% Part ((1) Input an expression for the charge on the capacitor as a function of time. '1\"): (l-e'llt'T0):\"'T))' E0 1: e t X Submit Hint | I give up! Hints: deduction per hint. Hints remaining: i Feedback: deduction per feedback. $3 10% Part ('5') For the time period While the capacitor is discharging, What is the magnitude of the maximum value of the current? lImaxl : VOIR X Attempts Remain $2 10% Part (1') Input an expression for the current as a function of time. You must write your expression in terms of Imax. I(t) = llmax| e( ("tt0\") a X Attempts Remain $2 10% Part (g) Enter an expression for the voltage measured across the resistor, VR, as a function of time. VB\") =V0 e' ( { t to )9'1 ) X Attempts Remain Feedback: is available. $8 10." art (h) Enter an expression for the maximum voltage measured across the capacitor._VmX, during the period of time starting with the switch being moved tiposition ". Vm : \\10 x Feedback: is available. [+3 10% Part (i) Enter an expression for the voltage measured across the capacitor. VG, as a function of time. Your expression must be in terms of the Vmax entered in the previous step. 10% Part ( j) Which choice correctly expresses the sum of the voltages across the resistor and the capacitor as a function of time. V}; + VC? 0 J Correct