Three capacitors and a battery are connected to a battery and a switch S, as sho

Question

Three capacitors and a battery are connected to a battery and a switch S, as shown. Initially capacitor 1 is connected to the battery and capacitors 2 and 3 are uncharged. Let C_1 = 10^-6 F, C_2 = 2timesl0^-6 F, and C_3 = 3times10^6 F and V= 12 V. a) How much charge is stored on capacitor C_1? b) The switch is then thrown to position "b". What will the new charge be on capacitor C_1? c) What will be the voltage across capacitor C_2? d) How much energy will be lost by the system when the switch is thrown from position "a" to position "b"?

Explanation / Answer

Note:C2=2*C1 and C3= 3*C1

a) the charge on C1 is given by Q = C1*V = 12*10^-6 = 12uC

b)let the charges be q1 q2 and q3.and voltage across all three be x(since they are in parallel the voltages are equal)

then since charge is conserved

q1+q1+q3 = 12uC

or

C1*x+2*C1*x+3*C1*x=12uC

x = 12uC/(6*C1)=2V

so charge on C1 = C1*x = 10^-6*2=2uC

d) energy would not be lost as there is no resistance in the system and ideal capacitors are loss less.

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