Equivalent Capacitance and Resistance of this Circuit

[goutes1234]

Homework Statement

Hello, I am trying to find the Equivalent Capacitance and Resistance of this Circuit

Relevant Equations

Ceq=1/C+(1/C)... (series) Ceq=C+C...(parallel
Same for resistors

NOTE: THE C1 that is 120 microfarads is meant to be C3.
What I did first was find equivalent capacitance of C2 and C3 by doing (40)*(120)/(40+120)=30. Then I found Ceq by doing (20)*(30)/(20+30)=12. For the resistance I did 6*3/(6+3)=2, for R2 and R1. Then to find Req I did (5)*(2)/5+2= 10/7

Am I correct.

 

[BvU]

Hello @goutes1234 ,

$\qquad$!​

Homework Statement:: Hello, I am trying to find the Equivalent Capacitance and Resistance of this Circuit

And why would you want to do that ? What is the actual text of this exercise ?
What is going to happen after the switch is closed ?

Relevant Equations:: Ceq=1/C+(1/C)... (series) Ceq=C+C...(parallel
Same for resistors

Oops... Same ?
And: if it's true for resistors, and something similar is true for capacitors $--$ then what are you going to do with a mixture of R and C ?

$\$

 

[goutes1234]

Hello @goutes1234 ,

$\qquad$!​

And why would you want to do that ? What is the actual text of this exercise ?
What is going to happen after the switch is closed ?
Oops... Same ?
And: if it's true for resistors, and something similar is true for capacitors $--$ then what are you going to do with a mixture of R and C ?

The goal is to simplify the circuit into something less complicated. For example, just one capacitor and one resistor along with the switch and EMF source.

 

[berkeman]

The goal is to simplify the circuit into something less complicated. For example, just one capacitor and one resistor along with the switch and EMF source.

Well, if you have two capacitors in series with a resistor, you may be able to simplify that leg by combining the two capacitors (using the correct series-combination formula for capacitors). But in general if you have two parallel legs with each having an R and a C, how can you combine those into a single R and C? I'm not sure it can be done.

If you write the KCL equations for that circuit using the differential equation for the capacitors, I think the overall transfer function you get will be more complex than just a single equivalent R and C...

 

[goutes1234]

Well, if you have two capacitors in series with a resistor, you may be able to simplify that leg by combining the two capacitors (using the correct series-combination formula for capacitors). But in general if you have two parallel legs with each having an R and a C, how can you combine those into a single R and C? I'm not sure it can be done.

If you write the KCL equations for that circuit using the differential equation for the capacitors, I think the overall transfer function you get will be more complex than just a single equivalent R and C...

Ah I see. Well, if you were to calculate the equivalent capacitance and equivalent resistance, it is possible to do so no? I am just wondering if I am using the rules of parallel and series correctly?

 

[berkeman]

I am just wondering if I am using the rules of parallel and series correctly

When you calculated the series combination of the two capacitors on the same leg, you got the correct answer (but you should have included the units uF to be more clear):

(40)*(120)/(40+120)=30

After that, I don't seen any valid series/parallel combinations that can be done.

If the problem were about a single frequency, you could use phasor addition to calculate the overall phasor impedance at that frequency. But this problem is a transient analysis with the switch closing, so I think you need to use KCL and differential equations to solve for the transient response...

 

[BvU]

What is going to happen after the switch is closed ?

Would equivalent resistance/capacity help you there ?

$\$

 

[goutes1234]

Would equivalent resistance/capacity help you there ?

$\$

yes it would

 

[goutes1234]

When you calculated the series combination of the two capacitors on the same leg, you got the correct answer (but you should have included the units uF to be more clear):

After that, I don't seen any valid series/parallel combinations that can be done.

If the problem were about a single frequency, you could use phasor addition to calculate the overall phasor impedance at that frequency. But this problem is a transient analysis with the switch closing, so I think you need to use KCL and differential equations to solve for the transient response...

hmmm. there has to be a way to simplify it down as the problem is trying to find the current through the resistor. as well as the charges on the capacitors.

 

[berkeman]

Also, a small tip about drawing schematics (if you were the one who drew the circuit). Watch out for connection dots in strange places, because it can be an indication of an error in the connections. The dots should only show up in orthogonal connections, when using most schematic capture packages. The dot on the lower resistor connection indicates that the wire was drawn too far to the left -- it should instead terminate on the end of the resistor (where the dot is currently indicating a connection). In this case, a proper connection was made, but most design rules check routines would flag it at least with a warning.

 

[berkeman]

hmmm. there has to be a way to simplify it down as the problem is trying to find the current through the resistor. as well as the charges on the capacitors.

You can find that with KCL and $i(t) = C \frac{dv(t)}{dt}$

 

[goutes1234]

You can find that with KCL and $i(t) = C \frac{dv(t)}{dt}$

how would you go about that, I am lost there.

 

[berkeman]

Have you learned how to use KCL to solve for circuit voltages and currents?

Have you learned how to use that differential equation relating i and v for capacitors? You have probably at least solved for the time constant of a simple RC circuit, right?

 

[goutes1234]

Have you learned how to use KCL to solve for circuit voltages and currents?

Have you learned how to use that differential equation relating i and v for capacitors? You have probably at least solved for the time constant of a simple RC circuit, right?

so far, only was taught how to simplify circuits through series and parallel. Once I arrive at that I believe I know how to do the rest. If I find the equivalent capacitance I will share more.

 

[goutes1234]

Have you learned how to use KCL to solve for circuit voltages and currents?

Have you learned how to use that differential equation relating i and v for capacitors? You have probably at least solved for the time constant of a simple RC circuit, right?

ah yes i have learned it actually.

 

[Steve4Physics]

The goal is to simplify the circuit into something less complicated. For example, just one capacitor and one resistor along with the switch and EMF source.

So, just to confirm, the complete and accurate homework statement is “Simplify the given circuit into something less complicated”.

Is that the full assignment? Note that @BvU already asked (Post #2) “What is the actual text of this exercise?“ but you have not yet answered.

 

[goutes1234]

So, just to confirm, the complete and accurate homework statement is “Simplify the given circuit into something less complicated”.

Is that the full assignment? Note that @BvU already asked (Post #2) “What is the actual text of this exercise?“ but you have not yet answered.

the goal of the assignment is to find the equivalent capacitance and the equivalent resistance. Once I find those, I am given formulas to calculate current through the resistors and charges on the capacitors.

 

[vela]

I think what people are asking is what the actual text of the problem is, not what you think the text means. What you're claiming the problem is asking for doesn't make sense for the given circuit. Other than the simplification of combining the two capacitors in series, there's nothing else you can do to simplify the circuit.

 

[goutes1234]

I think what people are asking is what the actual text of the problem is, not what you think the text means. What you're claiming the problem is asking for doesn't make sense for the given circuit. Other than the simplification of combining the two capacitors in series, there's nothing else you can do to simplify the circuit.

the question shows that graph, and is asking to find the current through the resistors and the charge on the capacitors at t=0 when switch is closed.

 

[vela]

the question shows that graph, and is asking to find the current through the resistors and the charge on the capacitors at t=0 when switch is closed.

By graph, are you referring to the schematic?

The actual question suggests a different approach than the one you were taking. This is the reason we ask students provide the exact text of the problem statement.

Before the switch is closed, it's safe to assume all of the capacitors are uncharged. You should've learned about how the voltage across a capacitor can vary with time. Use this fact to deduce the voltage across the capacitors immediately after the switch is closed.

 

[cnh1995]

@goutes1234,
If the question only asks about the current through different resistors and charge on the capacitors specifically at t=0 when the switch is closed, then finding equivalent capacitance/resistance of the circuit is not the way to go.

You need to focus only on the instant when the switch is closed, and the behavior of the components in response to that.
Do your notes/textbooks have any information on this?

 

[berkeman]

You need to focus only on the instant when the switch is closed

Hey! Look who's back!

 

[Steve4Physics]

the goal of the assignment is to find the equivalent capacitance and the equivalent resistance. Once I find those, I am given formulas to calculate current through the resistors and charges on the capacitors

the question shows that graph, and is asking to find the current through the resistors and the charge on the capacitors at t=0 when switch is closed..

Since you won’t tell us what the exact question is, I thought it might help if I attempted to formulate it. From what has been said so far, I think the question is this:

In the circuit (shown in Post #1) the capacitors are initially uncharged. The switch is closed at time t=0. Find the current through each resistor and the charge on each capacitor at time t=0.

Can you confirm that this is the complete question (or is equivalent to it)?

 

[DaveE]

the question shows that graph, and is asking to find the current through the resistors and the charge on the capacitors at t=0 when switch is closed.

Please post the exact wording of the question. It may be that whoever created this problem doesn't know what they are doing.

Again, this question doesn't make sense with that network. Specifically, the charge on each of the capacitors is undefined at t=0 (i.e. it could be anything). The charge on C2 and C3 (individually) is always undefined since they are in series. Note that you do know that the sum of the voltages on C2 & C3 is zero before t=0, since they can discharge through R2.

Then, because you don't know the charge on C1 at t=0, the currents are also undefined at t=0.

 

[tech99]

This is my suggestion. At switch on, the capacitors provide no opposition to the flow of current, so the resistors may be considered alone. The total resistance is 5 + (3x6)/(3+5) = 7.25 Ohms.
After a long time, the charging current falls to "zero". C1 and C2 do not retain any charge as they have a resistor across them. So we have only C1 of 20uF in circuit.
So the equivalent circuit is 20uF in series with 7.25 Ohms.

 

[Steve4Physics]

The total resistance is 5 + (3x6)/(3+5) = 7.25 Ohms.

You mean 5 + (3x6)/(3+6) = 7 ohms.

After a long time, the charging current falls to "zero". C1 and C2 do not retain any charge as they have a resistor across them. So we have only C1 of 20uF in circuit.
So the equivalent circuit is 20uF in series with 7.25 [should be 7] Ohms.

This implies that the current through the supply, as a function of time, is the same as you would get if the resistors and capacitors were replaced by a single 20μF capacitor in series with a single7Ω resistor.

This would mean that the circuit behaviour (during charging) is totally unaffected by the values of C2 and C3. I don't think that can be correct.

In addition, we don’t actually know what the real question is. There may be no need to find any ‘equivalent’ values, even if it is possible.

 

[Delta2]

I think tech99 wants to say that only at the moment t=0 the circuit is equivalent to a 20μF capacitor in series with a 7Ohm resistor

 

[DaveE]

I think tech99 wants to say that only at the moment t=0 the circuit is equivalent to a 20μF capacitor in series with a 7Ohm resistor

OK, but, in an equivalent circuit, if you can ignore C2 & C3 at t=0 you can also ignore the value of C1. But you still don't know how much voltage is applied across that 7ohm equivalent at t=0 without knowing the charge on C1.

Honestly, I think it's a waste of time to discuss a poorly phrased question until we get some clarification of what they are looking for.