10 F01 210 t?dep 18330982 (c) What are the charges on the inner and outer surfac

Question

10 F01 210 t?dep 18330982 (c) What are the charges on the inner and outer surfaces of the aluminum spherical shelir Qimner Qouter n the figure below, capadtor 1 (C-27 uF) initially has a potential difference of 60.0 V and capacitor 2 (C -5.10 HF) has none. The switches are then closed simul Ct (a) Find the final charge on each capacitor after a long time has passed. (b) Calculate the percentage of the initial stored energy that was lost when the switches were closed Show all Physiss 21 F201.htm $18E&M-HW-2.html;

Explanation / Answer

a) resultant potential after closing the switching V = (C1V1+C2V2) / C1+C2

V= (27*10-6*60 + 5.10*10-6*0) / (27*10-6 + 5.10*10-6)

V= 50.46 volts

Now, using Q=CV

charge at C1, Q1= 27*50.46 uC = 1362.6 uC

charge at C2, Q2= 5.10*50.46 uC = 257.34 uC

b) Ei = (0.5C1V12+0.5C2V22) { Here V1 and V2 are the initial potential of the corresponding capacitors}

Ef= 0.5(C1+C2)V2 { here V is the common potential after switching on the switches}

loss = Ei - Ef

loss = (C1C2(V1-V2)2)/ 2(C1+C2) = (5.10*27*10-12(60-0)2)/2(5.10*10-6+27*10-6)

loss = 7727.49* 10-6 joules

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