How much charge does a 16 V battery have to supply to fully charge a 2.2 F capac

Question

How much charge does a 16 V battery have to supply to fully charge a 2.2 F capacitor and a 4.7 F capacitor when they’re in parallel

q=110uC

How much energy does the battery have to supply in this case?

How much charge does a 16 V battery have to supply to fully charge a 2.2 F capacitor and a 4.7 F capacitor when they’re in series?

q=110uC

How much energy does the battery have to supply in this case?

How much charge does a 16 V battery have to supply to fully charge a 2.2 F capacitor and a 4.7 F capacitor when they’re in series?

Explanation / Answer

Hi,

Well according to what is written I think there are three questions:

1) The charge when two capacitors of known capacitance are in parallel and are charged by a battery of known voltage.

2) The energy spend by a battery of known voltage to charge two capacitors, given the charge.

3) The charge when two capacitors of known capacitance are in series and are charged by a battery of known voltage.

So to solve the first question we should remember that the voltage is same for every capacitor if they are in parallel and the charge is distributed through them, so we could find the charge using this equation:

Qt = Ceq * V ; where V is the voltage of the battery, Qt is the total charge supplied and Ceq is the equivalent capacitance which is the sum of the individual capacitances.

So : Ceq = C1 + C2 = (2.2 + 4.7) F = 6.9 F ;   Qt = (6.9 F )*(16 V) = 110.4 C

For the second question we should think of something. The charge that the battery spend to charge the capacitors should be kept by them in the form of potential electric energy, therefore if we find this energy we can solve the question.

Using some calculus and the definition of work in terms of potential energy, as well as the definition of voltage in terms of capacitance and electric charge we have the following equation:

U = Q2/(2*Ceq ) = (110 C)2 / (2*6.9 F ) = 8.8*10-4 J

For the final question we only have to remember that when the capacitors are in series the charge is the same for any of them, but the total voltage is splited between them so a new way to find the equivalent capacitance is in order.

This new way is : (1/Ceq ) = (1/C1) + (1/C2) , so (1/Ceq ) = 1/2.2 + 1/4.7 = 0.667 which implies that Ceq = 1.5 F

Once we have the equivalent capacitance we proceed as before:

Qt = (1.5 F )*(16 V) = 24 C

I hope it helps

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