Question

V 2R 2C Q4 -Ch26 Given the circuit in the figure, answer the following in terms of V,R,C. (a) What is the potential of point a with respect to point b when the switch (S) is open? (b) What is the final potential of point b with respect to the ground when Sis closed, and equilibrium is reached? (c) How much does the charge on each capacitor change when S is closed, and equilibrium is reached? b S с + R

Answer 1

(a) when No urlent passes s is open, resistons 2R andR 20 through the Hen voltage drops acros c and 2c is viev = v=V v = va-o = V = Va=v and v. = V-V =) = 0. ac potential of a with respect bis Vans no ulreal- (b) of switch is closed theen passes through capacitors C and 2c. Total current through both resistors Hence. is N А QRIR 3R V V = 8 (2R) = (2R) 2v 3 3R ir = V (R) R ak 3R 3 *- = Y = } - {% = x

before closing kuitch, C is a = - CV on 2c 2 3 quitially, charge on Charge is a = 2cv. Total charge q=9, +4=3 cv. After cloring switch Charge anc is a = c/%) = c) = cv Au = a(ch charef on ac is al = 20 (32) = 20 (2x ) = 4 cu A = 20v-4cv = zer) Total charge q: alta' = ev + 5cv = 2ev. Aq e 90-9' = 3CV – 2CV = CV cv-CV = 2 3