# Charging a Capacitor with Another Capacitor

• breez
In summary, the conversation discusses the writing of a differential equation to find the charge on a 4 microF capacitor as a function of time, as well as clarifying a typo in the given circuit diagram. The conversation also touches on the arrangement of the capacitors in the circuit, with the conclusion that they are in parallel when the current goes to zero.
breez
http://img230.imageshack.us/img230/8480/circuitbb5.th.gif

Switch 1 is turned on until the 12 microF capacitor is completely charged. Then Switch 1 is switched off, while switch 2 is switched on.

How do you write a differential equation that may be used to find charge on the 4 mircroF capacitor as a function of time?

My attempt:

Applying Kirchhoff's Loop Rule: $$0 = V_1 - R_1 \frac{dq}{dt} - R_2 \frac{dq}{dt} - \frac{q}{C_2}$$, where q is the charge on the 4 microF capacitor.

This can be rewritten as
$$0 = \frac{Q-q}{C_1} - \frac{dq}{dt} (R_1 + R_2)- \frac{q}{C_2}$$

In this last step I assumed the charged discharged from the 12 microF capacitor is the charge that appears on the 4 microF capacitor.

(loops used are clockwise)

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What does the $$\mbox{20M} \Omega$$ refer to? How can a voltage source have such a high resistance? The voltage provided by the source isn't given as well. Looks like there's something wrong with the picture.

Yeah that's a typo in the book. It should be 20MV.

a. What is the charge on the 4 microF capacitor after switch 2 is closed for 1 minute?

b. What is the final charge on the 2 capacitors?

Hi breez,

I think your differential equation is okay; and you don't need the differential equation to solve for part b.

Oh thanks. Are these 2 capacitors in series or parallel? I think they should be in series right?

EDIT: Actually after solving this problem the capacitors end up with different charges and different voltages I find they are in fact parallel...

I guess as long as 2 capacitors are in a closed loop, they must be in parallel since their 2 ends are at the same 2 voltages.

This is kind of counterintuitive because they seem to be in series...

So another requirement for them to be in series is not only for them to flow into one another, but for their ends to be at a different voltage right?

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They are not in series; in series capacitors have the positive plate of one capacitor attached to the negative plate of another.

Normally they are also not in parallel, since their voltages are not the same. When the current goes to zero, however, the potential differences across the resistors will vanish and at that point they can be treated as if they are in parallel.

## 1. How does charging a capacitor with another capacitor work?

When two capacitors are connected in series, the electric charge on one capacitor can flow to the other capacitor, causing the second capacitor to gain charge. This is known as capacitance coupling and is based on the principle that the electric field between the two capacitors allows for the transfer of charge.

## 2. Can I use capacitors with different capacitance values to charge each other?

Yes, you can use capacitors with different capacitance values to charge each other. However, the resulting voltage across each capacitor will not be equal. The larger capacitor will gain more charge and have a higher voltage, while the smaller capacitor will have less charge and a lower voltage.

## 3. How long does it take to charge a capacitor with another capacitor?

The time it takes to charge a capacitor with another capacitor depends on the capacitance and voltage of both capacitors, as well as the resistance of the circuit. A higher capacitance or voltage will result in a longer charging time, while a lower resistance will speed up the process.

## 4. What happens if I try to charge a capacitor with another capacitor without a circuit?

Without a circuit, the two capacitors will not be able to transfer charge to each other. A circuit is needed to allow the flow of electric current between the two capacitors. Without a circuit, the charge on the capacitors will remain the same.

## 5. Is it possible to fully charge a capacitor using another capacitor?

No, it is not possible to fully charge a capacitor using another capacitor. The maximum voltage that can be achieved when charging a capacitor with another capacitor is equal to the sum of the individual capacitor's voltages. This is known as the principle of superposition.

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