Conversation started Jul 18, 2019 at 10:56.
Jul 18, 2019 10:56
@JohnRennie hi.
@Nobodyrecognizeable hi
@JohnRennie how should I distinguish series and parallel dielectrics?
@Nobodyrecognizeable The two capacitors in the diagram have the same capacitance.
@JohnRennie all right. But how these could be connected in parallel?
@Nobodyrecognizeable they aren't connected in parallel ...
Jul 18, 2019 11:01
@JohnRennie that's why I'm asking you to help connecting them in parallel.
I'm not sure what you are asking. Are you trying to answer the question you show?
@JohnRennie all right the capacitance should be { $\epsilon_0/{1/k_1+1/k_2}$}
Well it's just two capacitors in series so the total caapcitance is $1/C = 1/C_1 + 1/C_2$ where $C = \epsilon A/d$.
@JohnRennie yep sorry.
@JohnRennie can I ask another one?
The thing you need to know is that the right diagram, with the two dielectrics directly in contact, is the same as the left diagram with two separate capacitors.
Jul 18, 2019 11:08
@JohnRennie OK.
@Nobodyrecognizeable is it obvious why they are the same, or should I explain it?
Which do you want to do first?
@JohnRennie they're connected to same battery terminals so equal charge in fig 1 in 2nd they are kept in contact to share equal charges.
@JohnRennie 6a
So 6a with the switch open. Let's redraw the circuit to make it clearer ...
Jul 18, 2019 11:13
@JohnRennie yep.
@JohnRennie OK.
@Nobodyrecognizeable That's 6(a) with the switch open. Yes?
No current is flowing because DC current can't flow through the capacitor C1. Yes?
@JohnRennie OK I'm verifying.
@JohnRennie yes.
So if no current is flowing the voltages across the two resistors must be zero because for a resistor V=IR.
R1, R2 and C2 are in series, so the total voltage across them has to 90V. Since the voltage across the two resistors is zero that means the voltage across C2 must be 90V.
(I've just realised I mislabelled my diagram. The lower capacitor is C2.)
Jul 18, 2019 11:22
@JohnRennie just a symbol mistake. I didn't even recognised that:) -
There :-)
@JohnRennie so 0V for C2
@JohnRennie next time the resistor also comes in place as well
@Nobodyrecognizeable 0V for C1 i.e. 0V for the 6uF capacitor.
@Nobodyrecognizeable That's with the switch closed. Now, what is the current?
@JohnRennie the capacitors should be short circuited? As per transient analysis.
@Nobodyrecognizeable Remember that no current flows through the capacitors, so all the current flows through the resistors.
We are after the equilibrium charges and voltages i.e. a long time after the switch has been closed.
At least, the question doesn't say immediately after closing the switch
Jul 18, 2019 11:30
So the current is 90/300. V is 30 for each.
@JohnRennie I am sorry they should be short circuited after a long time as per transient analysis.
Yes. And C1 and C2 are in parallel with R2 and R3, so the voltage across C1 must be the same as the voltage across R2, and the voltage across C2 must be the same as the voltage across R3.
@JohnRennie in second case current should be zero in middle branch as infinite resistance?
@JohnRennie yep....
So both capacitors have a voltage of 30V across them.
1 min ago, by Nobody recognizeable
@JohnRennie in second case current should be zero in middle branch as infinite resistance?
@JohnRennie or just the capacitor of 1$\mu F$ should be excluded?
@Nobodyrecognizeable I don't understand what you are asking there? What do you mean by the middle branch?
Jul 18, 2019 11:37
@JohnRennie I am asking the next question. Sorry ie figure 4.34b
Ah, are you now looking at the second circuit?
@JohnRennie yep.
For the second circuit with the switch open the current in the middle branch is indeed zero.
And the current in the top branch is also zero.
So no current flows, and that means the voltages across all resistrs is zero.
@JohnRennie I have seen it but never solved problems on them
@JohnRennie 6$\muF$ has 25V and 2$\muF$ has 75 V. So what's next?
Jul 18, 2019 11:46
@Nobodyrecognizeable and this is the circuit with the switch closed:
@JohnRennie what happened?
@Nobodyrecognizeable I mislabelled one of the capacitors. It's correct now.
Can you do this one on your own?
5 mins ago, by Nobody recognizeable
@JohnRennie 6$\muF$ has 25V and 2$\muF$ has 75 V. So what's next?
Please sort this out. @JohnRennie
@JohnRennie yep. I will try.
@Nobodyrecognizeable yes, that's correct for the switch open. So you've answered the question haven't you? Now you know the voltages the charge is just $Q = CV$.
@JohnRennie yes. How to solve for potential of A?
Jul 18, 2019 11:51
Ah, yes, well if the voltage at the bottom end of C3 is zero, and the voltage drop across C2 is 75V, then the voltage at the other end of C2 must be 75V. Yes?
Or look at it this way. The voltage at the top end of C2 is +100V, and the voltage drops by 25V across C2 so the voltage at the bottom end of C2 is 100 - 25 = +75V.
Both approaches give the same voltage of +75V at the point A.
 
Conversation ended Jul 18, 2019 at 11:52.