Analyzing a circuit with 1 point earthed

Krushnaraj Pandya

Gold Member
1. The problem statement, all variables and given/known data
Find potential of A and B in the given figure. (pardon poor quality, I only have a webcam)

2. Relevant equations
All related

3. The attempt at a solution
marking 1 to 4 from left to right. C1,C2,C3 are in series. C123=(2/3)C. which is in parallel with C4. C effective is 5C/3. What now? I don't know what to make of the point between them (lets call it D) being earthed.

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CWatters

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The voltage across a resistor at time t depends on the current at time t, however the voltage across a capacitor depends on past current so you need to make some assumptions about how the system starts off.

There is only one connection to earth so what does that mean for the current flowing to/from earth?

Krushnaraj Pandya

Gold Member
The voltage across a resistor at time t depends on the current at time t, however the voltage across a capacitor depends on past current so you need to make some assumptions about how the system starts off.
Usually with such problems in my textbook we are supposed to assume we just put the circuit in place.

CWatters

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Usually with such problems in my textbook we are supposed to assume we just put the circuit in place.
Ok so if the capacitor came out of it's box with some random voltage on it this problem would be impossible to solve. Try assuming they all start with 0V across each when the battery is connected.

Krushnaraj Pandya

Gold Member
Ok so if the capacitor came out of it's box with some random voltage on it this problem would be impossible to solve. Try assuming they all start with 0V across each when the battery is connected.
I already have...I don't understand from there what I can do when a point is earthed after I find effective capacitance

CWatters

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Sorry I added this bit to the question above...

There is only one connection to earth so what does that mean for the current flowing to/from earth?

CWatters

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marking 1 to 4 from left to right. C1,C2,C3 are in series. C123=(2/3)C. which is in parallel with C4.
C1,2,3 are in series with each other and in series with C4.

What do you know about the current through components in series?

Krushnaraj Pandya

Gold Member
C1,2,3 are in series with each other and in series with C4.
I understand C 1,2,3 are in series with each other but how are they in series with C4. Did you mean to say parallel, since they are connected across the same potentials of 10 and zero?

CWatters

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No I do mean series. For components to be in parallel they must share two nodes.

The equivalent capacitance of C1-3 is connected to earth and the -ve of the battery.
C4 is connected to earth and the +ve of the battery.

So they only share one node (earth).

Delta2

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Cwatters is trying to say that the current from the earthed point to the ground will always be zero, so essentially all the capacitors are in series.

BUT I have trouble myself understanding why that current will always be zero.

CWatters

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In order to make progress I'll give you two hints...

There is only one connection to earth so no current flows through that connection to earth.

All 4 capacitors are in series with the battery so when the battery is connected the same amount of charge flows through all 4 capacitors. This continues until the sum of the voltages on each capacitor add up to the battery voltage (eg Kirchoff's voltage law).

Krushnaraj Pandya

Gold Member
No I do mean series. For components to be in parallel they must share two nodes.

The equivalent capacitance of C1-3 is connected to earth and the -ve of the battery.
C4 is connected to earth and the +ve of the battery.

So they only share one node (earth).
is there a way I can develop this intuition? a link perhaps...
current is same across series. Therefore charge on capacitors will be the same. Adding C 1,2,3,4 in series, equivalent capacitance is 2C/5, using Q=CV, total charge on each capacitor is 4C. Correct?
I don't know how to proceed further, shouldn't potential at A be 10 V itself since there is no capacitor till that point

Krushnaraj Pandya

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Alright, so I know the potentials across each capacitor now. From 1 to 4 they are 2,2,2 and 4 V

Krushnaraj Pandya

Gold Member
How do I derive potentials at A and B from this?

CWatters

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I haven't checked the voltages you calculated but...

If the voltage across C4 is 4v and the left hand side is connected to earth (0V) then the right hand side of C4 must be at -4V.

Edit: ok I agree your voltages are correct.

Krushnaraj Pandya

Gold Member
I haven't checked the voltages you calculated but...

If the voltage across C4 is 4v and the left hand side is connected to earth (0V) then the right hand side of C4 must be at -4V.
The answer says +4V, also at point A, the answer says the potential is -6V. This is just a mirror to what you said, though. Can you explain how you got this?

Delta2

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maybe we need to remind you that the potential difference across any type of lumped element between points A and B is $V_{AB}=V_A-V_B$ where $V_A$ and $V_B$ the potentials at points A and B respectively. So you know all the potential differences and also that the potential at the earth point (lets name it C) is $V_C=0$. You also know $V_{BC}$ for example, so...

CWatters

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Sorry I got the battery voltage wrong way around. Book answer is correct.

Krushnaraj Pandya

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Do we consider the negative terminal of the battery at -10V?

Krushnaraj Pandya

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since there seems a gradual increase to zero till the earthed point. and then again from 0 till +10 to the positive terminal

Krushnaraj Pandya

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can you explain again why no current flows into the earth?

Delta2

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if you consider the negative terminal at -10V and the positive terminal at +10V then the potential difference across the source would be 10-(-10)=20V...

Krushnaraj Pandya

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if you consider the negative terminal at -10V and the positive terminal at +10V then the potential difference across the source would be 10-(-10)=20V...
this seems counter-intuitive but undeniably correct. How can I easily understand that the sign of potential at A is negative, and at B is positive. You mention that we know potential at earth is 0 and we got the potential differences correctly too. Then whats to stop the point at B from having a potential -4 V?

Delta2

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this seems counter-intuitive but undeniably correct. How can I easily understand that the sign of potential at A is negative, and at B is positive.
You can understand or infer that, all you can infer is because B is connected at the positive terminal will have a higher potential than A which is connected at the negative terminal, it might as well both potential be negative with $V_B=-1V >-11V=V_A$, $V_{BA}=V_B-V_A=-1-(-11)=+10V.$
You mention that we know potential at earth is 0 and we got the potential differences correctly too. Then whats to stop the point at B from having a potential -4 V?
Because it is $V_{BC}=V_B-V_C=4V$

Krushnaraj Pandya

Gold Member
You can understand or infer that, all you can infer is because B is connected at the positive terminal will have a higher potential than A which is connected at the negative terminal, it might as well both potential be negative with $V_B=-1V >-11V=V_A$, $V_{BA}=V_B-V_A=-1-(-11)=+10V.$

Because it is $V_{BC}=V_B-V_C=4V$
Got it! Thank you, I just realized that I learned Kirchhoff's laws on PF even though they are in the next chapter hehe
Thank you very much @CWatters for your help (although I'd still like to know why no current flows to the earth)

"Analyzing a circuit with 1 point earthed"

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