How Do You Calculate the Potential Difference Across a Capacitor in a Circuit?

[Prannoy Mehta]

Homework Statement

Find the potential difference across the 2 microfarad capacitor. A 24V battery's negative end is connected to a 2 microfarad capacitor, which is connected to the negative end of a 12V battery. Which is further(The positive end) connected to a 4 microfarad capacitor, and it is connected to the 24V battery's positive end.

Homework Equations

Kirchoff's Loop Law.

The Attempt at a Solution

The only one equation I got is @Q1+Q2=48*10^-6

 

[haruspex]

Please define Q1 and Q2 and post your working.

 

[Prannoy Mehta]

Let Q1 is the charge stored in the 2 microfarad capacitor, and Q2 is the charge stored in the 4 microfarad capacitor.

Q1/2*10^-6 + Q2/4*10^-6 +12-24=0
=>Q1/2*10^-6 + Q2/4*10^-6=12
=>2Q1+Q2=48*10^-6

I am not sure how to proceed later on, or if possible an alternate approach.

 

[Orodruin]

Do you think the capacitors can store different amounts of charge?

 

[Prannoy Mehta]

I think it does, as they are of different capacitance.
My other doubt was, that negative terminal of a battery, 12V and 24 V connect the 2 microfarad capacitor, should it not be 0. ? The 4 microfarad capacitor gets a 12V potential difference across, it's ends.

My concepts are not that great, when it comes to capacitors, I can't fully understand it. It would be great, if you could help me in understanding how to go about the topic.

Final answer was given as 8V.

Thank you in advance.

 

[Orodruin]

I think it does, as they are of different capacitance.

How do the capacitors receive their charge?

 

[Prannoy Mehta]

In a general situation, when there is potential difference across the plates. The electrons of the plate connected to the higher potential move towards to the higher potential. Whereas the electrons from the lower potential charge go to the negative terminal ?

 

[Prannoy Mehta]

lower potential go to the negative terminal *

 

[Orodruin]

How does it relate to the total current that has come through the capacitor?

 

[Prannoy Mehta]

I am not sure how to answer is this question.

 

[Orodruin]

If a 1 A current passes a capacitor for 1 s, what is its charge?

 

[Prannoy Mehta]

Depends on the capacitance and potential difference ? Q=CV ?

 

[Orodruin]

Depends on the capacitance and potential difference ? Q=CV ?

No, it does not depend on the capacitance, or the potential. The resulting potential difference will be decided by the charge.

 

[Prannoy Mehta]

I din't get you.

 

[Orodruin]

I din't get you.

What is the definition of 1 C?

 

[haruspex]

I think it does, as they are of different capacitance.

Remember that the part of the circuit from one capacitor plate through the adjacent battery to the adjacent capacitor plate on the other capacitor is electrically isolated, i.e. its total charge cannot change. If the capacitors have different charges, what does that say about the net charge on the battery in between?

 

[Prannoy Mehta]

What is the definition of 1 C?

It is the charge carried by the current of 1A in 1 second.

Okay, I get bits of it. There is no current moving through the capacitor 2 microfarad. If no current moves from the 2 microfarad battery, no current moves from the 4 microfarad battery, if I am not wrong.

I would like to get this cleared to, is it right to say that the charge in a capacitor, and the charge moving through the capacitor are two different things.

 

[haruspex]

is it right to say that the charge in a capacitor, and the charge moving through the capacitor are two different things.

Certainly, since charge does not pass through a capacitor - it is not a conductor of DC.

 

[Prannoy Mehta]

Thank you, and sorry for the trouble I have caused both of you, Haruspex and Orodruin.

 

[haruspex]

Thank you, and sorry for the trouble I have caused both of you, Haruspex and Orodruin.

No trouble, it's what we're here for.