Equivalent capacitance problem

[gracy]

Basically I was saying I don't think we need a voltage source in order to determine the equivalent capacitance as ch1995 said not @gneill .Quotation is wrong.
As I have seen some problems in which I was asked to determine equivalent capacitance between two points and there was no voltage source.@gneill asked me to post those problems that's what I did.

 

[SammyS]

Yes,what is wrong in here?

Oh you edited that thread, Thread # 26. which originally said,

"But I have seen some problems in which I was asked to determine equivalent potential between two points and there was no voltage source."

 

[gracy]

Yes,I wrote potential instead of capacitance .See my post 33.

 

[SammyS]

I wrote that mistakenly.But my question is valid.

It would certainly help to have pointed out what the mistake was that was being referred to, and in post #26, when you edit the post, it helps to point out what change you make if the change is significant.

 

[epenguin]

Related to what I have advised before you need to be less plodding.
If I tell you the answer to this question (the one you started with) is obvious and not even needing to write down any calculations, does that make it obvious?

Relevant equations.

1. The potential drop (voltage as you and I naturally say, but I correct myself - pedantically) across a capacitor depends on some way or other that doesn't matter now on just the charge and capacitance, nothing else.

2. About the charges on capacitors in series we know something. Well we have gone into it recently so hopefully we do.

3. The capacitances are given in the problem. Is one, by any chance, related to another?

 

[cnh1995]

Then what voltage source does?

Suppose V=100V. In this problem, if you were asked to calculate the total amount of charge supplied by the source, you'll first calculate the equivalent capacitance between a and b (what you calculated earlier as 8μF ) and then use Q=C(eq)*V.. This is where adding a voltage source and calculating the equivalent capacitance matter. Because again, equivalent capacitance is always the one which is "seen" by a source connected between those points.

 

[gracy]

voltage divider

I want to know is voltage divider rule applicable only when two resistance are there in series,I never found R3 in the below formula.I know that it is applicable for capacitors also what I am asking is it applicable only when two components are in series I know also that it is applicable in series connection only ,I am trying to stress on two

 

[epenguin]

I can probably guess what you're after with this question but shouldn't have to.

If you are asking whether there is any analogy between logic and equations of capacitors in series and resistors in series, yes there is a kind of analogy.

With resistors in series what is the physical quantity that is the same in each of them?

With capacitors in series what physical quantity is the same in each of them? - you have recently discussed this in detail.

If several equal resistors are in series how is the potential difference over each one related?

May be suggestive for your problem.

 

[cnh1995]

I want to know is voltage divider rule applicable only when two resistance are there in series,I never found R3 in the below formula.I know that it is applicable for capacitors also what I am asking is it applicable only when two components are in series I know also that it is applicable in series connection only ,I am trying to stress on two

Do you know how the formula for voltage divider is derived? Do you know Ohm's law?

 

[gracy]

Do you know Ohm's law?

$V$=$I$R

 

[cnh1995]

$V$=$I$R

Right. Now can you apply it to derive the voltage divider formula?

 

[gracy]

derive the voltage divider formula?

Vs = I × Rtot

However, we know that Rtot = R1 + R2 so we substitute this into the equation above to give the following expression.

Vs = I × (R1 + R2)

The above expression transposes to give the following expression for current.

I = Vs / (R1 + R2)

We know that the following expression for the output voltage is true.

Vo = I × R2

Substituting the previous expression for current into the above equation, we get the following.

Vo = Vs × R2 / (R1 + R2)

 

[gracy]

I think we can use it for any number of resistance.

 

[cnh1995]

Vs = I × Rtot

However, we know that Rtot = R1 + R2 so we substitute this into the equation above to give the following expression.

Vs = I × (R1 + R2)

The above expression transposes to give the following expression for current.

I = Vs / (R1 + R2)

We know that the following expression for the output voltage is true.

Vo = I × R2

Substituting the previous expression for current into the above equation, we get the following.

Vo = Vs × R2 / (R1 + R2)[/QUOT

I think we can use it for any number of resistance.

Exactly..

 

[gracy]

But it is derivation for resistance as we know ohm's law can't be applied for capacitors,how to derive this for capacitors?

 

[cnh1995]

But it is derivation for resistance as we know ohm's law can't be applied for capacitors,how to derive this for capacitors?

Use Q=CV. In series circuit, Q is same on each capacitor. Can you proceed from here?

 

[cnh1995]

But it is derivation for resistance as we know ohm's law can't be applied for capacitors,how to derive this for capacitors?

It will be not as straightforward as it is for resistors. Because resistors is series add directly while capacitors in series don't.. You can derive it but can't memorize it because it will change with number of capacitors.

 

[gracy]

Vo

What is Vo?

 

[cnh1995]

What is Vo?

Vo = I × R2

Voltage across R2..

 

[gracy]

In general?

 

[cnh1995]

In general?

In general it is the output voltage..

 

[gracy]

it is the output voltage..

Voltage across last resistance/capacitor?

 

[gracy]

Vs

Emf of battery?

 

[cnh1995]

Voltage across last resistance/capacitor?

Not last. It can be across any component. That depends on the problem. Here in this capacitance problem, Vo is voltage between c and d.

 

[cnh1995]

Emf of battery?

Right.

 

[gracy]

How to recognize output voltage?I thought it is Voltage across last resistance/capacitor.

 

[cnh1995]

How to recognize output voltage?I thought it is Voltage across last resistance/capacitor.

It is normally given in the problem itself.. However, the the terms input and output are commonly used in "systems" rather than in circuits like this. For example, power supply in our houses is Vin, the appliances connected to it are called 'load' and voltage across load is called output voltage.

Vo = I × R2

Here, R2 is the load.

 

[gracy]

Did not understand.

 

[gneill]

Gracy, what names you give to variables is not so important so long as you define them, are consistent in their use, and they convey some idea of what they are meant to represent. This just boils down to naming conventions for quantities. You can choose any variable names you want if you are so inclined, so long as you define them for your audience, usually by showing them on the circuit diagram.

It is typical to use $V$ for voltages, $I$ for currents, $R$ for resistances, and so on, and to give them subscripts or suffixes to distinguish them. Input or source voltages are often labelled $V_i$ or $V_s$ or $V_o$ (meaning "original" or initial value). What you want to take as an output voltage for whatever purposes you have at the time can be labelled any way you want, but common choices include $V_{out}$, $V_o$ (Yes, it can be used for both input or output labels, just not both at the same time!). Some people prefer to use U instead of V for voltages. It's a cultural thing. It should not cause confusion because variables should ALWAYS be defined before they are used!

Sometimes you want to reference a voltage across a particular component and then you might find it convenient to use, for example $V_{R1}$ or $V_{C3}$ where R1 and R3 are labelled components in your circuit diagram.

It's up to you to define your variables and labels for a given problem. If you are writing equations using variables then you should know what they represent beforehand because you have defined them. If you want to call the potential across any component the "output" of your circuit, that's entirely up to you. There is no strict rule about where that component has to be located in the circuit diagram (although most prefer to read circuit diagrams from left to right, top to bottom, input towards output. It's just a convention, and not a strict rule).

Above you presented a derivation for the voltage across a particular resistor in a voltage divider. You used variables R1, R2, Rtot, I, Vs and Vo. Each was clear in its use and intent, and you defined mathematically that Vo = I × R2 and correctly presented the finished expression. Yet now you are coming back to ask what the variables mean, and how to recognize the output? This doesn't make sense: You defined and used them yourself.

You can extend the voltage divider from two to any number of resistors and choose the potential across anyone of them to be your "output".

 

[cnh1995]

Did not understand.

Output voltage is the voltage across "expected" or "concerned" component. In your problem, C4 is the concerned component. It is specified in the problem.

 

[gracy]

Yet now you are coming back to ask what the variables mean, and how to recognize the output? This doesn't make sense: You defined and used them yourself.

Actually I copied it .

 

[cnh1995]

Actually I copied it .

Once you are done solving a number of problems, you'll be fluent in recognizing all that stuff and mainly, conventions.

 

[gracy]

I want to understand what the formula means how to use it

on the left side there is voltage across the numerator on right side.
V in is always the emf of source
and denominator on the right side would be sum of all the component(resistance or capacitor) present.
numerator on the right side is always the component (resistance or capacitor) across which we want to find the voltage i.e V present on left side.

 

[cnh1995]

I want to understand what the formula means how to use it

at the left side there will be voltage across the numerator on right side.
V in is always the emf of source
and denominator on the right side would be sum of all the component(resistance or capacitor) present.
numerator on the right side is always the component (resistance or capacitor) across which we want to find the voltage i.e V present on left side.

This formula is applicable only for resistors and not capacitors. I mean, you can't simply replace R1 with C1 and R2 with C2.

 

[cnh1995]

I want to understand what the formula means how to use it

at the left side there will be voltage across the numerator on right side.
V in is always the emf of source
and denominator on the right side would be sum of all the component(resistance or capacitor) present.
numerator on the right side is always the component (resistance or capacitor) across which we want to find the voltage i.e V present on left side.

Right. For resistors and inductors.