Question

r R ε с [7 points] 14. In the circuit shown above a battery with emf & and internal resistance r may be connected to a capacitor C through switch S. The switch may also connect the capacitor to resistor R. The capacitor is initially uncharged. Express your final answers only in terms of the variables €.r.C, R, and any necessary constants, as appropriate. a) At time t = 0, the switch is moved from the right to the left. What is the current passing through r at time t = 0? b) Determine an expression for the time it takes for the capacitor to reach 80% of its maximum charge. When the current through r is zero, the switch is flipped from the left to the right. Solve parts (c) and (d) after this event (the switch being flipped). c) Determine an expression for the current through the resistor R as a function of time. Show all work, beginning from fundamental laws or rules. (Hint: remember to express your final answer only in terms of the variables E,r, C, R, and any necessary constants... or in other words, don't write "Imax": d) On the axes below, sketch the current through R. Label at least one value on the vertical and horizontal axes. (These values should be expressed in terms of E,r, C, R, and any necessary constants only.) IR

Answer 1

s Ao) when switch is moved to left. capacitor is through battery Recall q = Cell- ē ce tloc) ४ w C МЛН R. So at t=0 q=0 Ans. 100 b.) {max- = CE so q= 80 ce = Oo8CE 100 Putting into -tlic 0.86€ = 5€ (1-ěthre) + こ 0.2 -t/c = Ino: a = -1.61 += 1o6182 Ans. Co When current through r = 0 q = CE on capacitor. - t/RC For discharging q = Cee so į = i = e -Elec d.) Ie 2012 Re RC t