Question

Because the system is isolated, the initial and final charges on the system must be the same. Use this condition and Equations (1) and (2) to solve for AVH (Use the following as necessary: C1, C2, and AV.): Qr = Q; → (C1 + C2)AV4 = (C1 – C2)AV; (C1 – C2)Vi AVF= (C1+C2) (3) (B) Find the total energy stored in the capacitors before and after the switches are closed and determine the ratio of the final energy to the initial energy. (4) U; = Use the equation for the energy stored in a charged capacitor to find an expression for the total energy stored in the capacitors before the switches are closed (Use the following as necessary: C1, C2, and AV.): Up = {G (AV)2 + {Cz(AV)2 = {(G + C2)(AV;)? Write an expression for the total energy stored in the capacitors after the switches are closed: Use the results of part (A) to rewrite this expression in terms of AV; (Use the following as necessary: C1, C2, and Av;.): (5) U = {{C} + C»)(40,12 Divide Equation (5) by Equation (4) to obtain the ratio of the energies stored in the system (Use the following as necessary: C1, C2, and AV.):

Answer 1

Of = 0; (6 + c) Ave = (+2) AV; Avf - (C1-C2) Avi cit C2 . Af = AVF - ( C - Ce) Avr C-C2 ) (462 U; = (Avo) 't § cz(Avs) (+e)(av)"} of C (AV) ² + + 2 C2 (AVE) =ž 6 +)(AVA)? + 6+ c) (since you y = 60-62)"@v,)?? С +С. Uf. - C1-cz)"@15+ *(6+c) (AV:)? Oi