What is the potential at the top of R2 in this circuit?

In summary: If the potential at the top of R3 is, say V3, and you "walk" from there across R2 which you say has a potential of V2 - V3, you'd get to the other side with a potential of V2 + V3. So there's a potential drop of 2V.
  • #1
marchcha
15
1

Homework Statement


A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 41 Ω, R3 = 68 Ω and R4 = 154 Ω. The capacitance is C = 49 μF and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.
h11_RC_time.png

What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?

Homework Equations


Kirchhoff's Laws

The Attempt at a Solution


I attempted to find Q(inf) by setting up kirchhoffs voltage and loop equations as shown:
1. I1 = I4
2. 14 = I2 + I3
3. V - I1R1 - I3R3 - I4R4 = 0
4. V - I1R1 - I2R2 - (Q/C) - I4R4 = 0

I used the equalities in equation 1 to solve equation 3 in terms of I3. I then used I3 from equation 3 and plugged it into equation 2 to get an equation for I2. I then plugged in what I got for I2 into equation 4 as well as plugging in I4 for I1. The final equation I got for the value of Q is: Q = C(V - I4R4 - (I4 - (V - I4(R1 + R4))/R3) * R2 - I4R4). I had already found the value for I4 in a previous problem using V = IR when the switch is closed for a very long time. I4's value is 0.54A.

Thank you so much in advance!
 
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  • #2
Hi marchcha,

You may be putting too much effort into this one :smile:

You're looking for the charge on the capacitor at steady state, Q(inf). What do you know about the value of the capacitor current ##I_c## at steady state? What does that tell you about the loop current for that loop?
 
  • #3
gneill said:
Hi marchcha,

You may be putting too much effort into this one :smile:

You're looking for the charge on the capacitor at steady state, Q(inf). What do you know about the value of the capacitor current ##I_c## at steady state? What does that tell you about the loop current for that loop?
The capacitors current will be zero at steady state. I'm a little confused as to what this tells us about the loop current for that loop.
 
  • #4
marchcha said:
The capacitors current will be zero at steady state. I'm a little confused as to what this tells us about the loop current for that loop.
Yes, ##I_c = 0## at steady state.

Is there any way to distinguish ##I_c## from the loop current? Aren't they identical? Just as the loop current for the first loop is identical to the currents flowing through the voltage source, R1, and R4.
 
  • #5
gneill said:
Yes, ##I_c = 0## at steady state.

Is there any way to distinguish ##I_c## from the loop current? Aren't they identical? Just as the loop current for the first loop is identical to the currents flowing through the voltage source, R1, and R4.
So would I2 also be 0?
 
  • #6
marchcha said:
So would I2 also be 0?
Yes. ##I2 = I_c = 0## at steady state.
 
  • #7
gneill said:
Yes. ##I2 = I_c = 0## at steady state.
So then Q = C (V - I1R1 - I4R4)?
 
  • #8
marchcha said:
So then Q = C (V - I1R1 - I4R4)?
Sure. Or Q = C*I3R3, to use your notation. You really don't need to invent so many different currents if there's just one loop current flowing...
 
  • #9
gneill said:
Sure. Or Q = C*I3R3, to use your notation. You really don't need to invent so many different currents if there's just one loop current flowing...
Ok, then how do you find I3?
 
  • #10
marchcha said:
Ok, then how do you find I3?
Draw in the current flowing through loop 1. It's the only current flowing at steady state.

upload_2017-2-16_16-50-58.png
 
  • #11
gneill said:
Draw in the current flowing through loop 1. It's the only current flowing at steady state.

View attachment 113321
Ok so I3 is .0456A I don't understand how the capacitors charge has anything to do with the first loop though?
 
  • #12
marchcha said:
Ok so I3 is .0456A I don't understand how the capacitors charge has anything to do with the first loop though?
If ##I_c = 0##, what's the current through R2? Hence, what's the potential drop across R2?
 
  • #13
gneill said:
If ##I_c = 0##, what's the current through R2? Hence, what's the potential drop across R2?
Zero for both.
 
  • #14
marchcha said:
Zero for both.
So if the potential drop across R2 is zero, what's the difference between the potential at the top of the capacitor and the potential at the top of R3?
 
  • #15
gneill said:
So if the potential drop across R2 is zero, what's the difference between the potential at the top of the capacitor and the potential at the top of R3?
Would it be just V?
 
  • #16
marchcha said:
Would it be just V?
er, no. If the potential at the top of R3 is, say V3, and you "walk" from there across R2 which you say has a potential drop of zero, what's the potential at the other end of R2 (also the top of the capacitor)?
 
  • #17
gneill said:
er, no. If the potential at the top of R3 is, say V3, and you "walk" from there across R2 which you say has a potential drop of zero, what's the potential at the other end of R2 (also the top of the capacitor)?
Ah so they'd be the same and you can say Q/C = I3R3 the equation above. Thanks!
 
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Related to What is the potential at the top of R2 in this circuit?

1. What is a two loop RC circuit?

A two loop RC circuit is a type of electrical circuit that consists of two resistors and two capacitors connected in a closed loop. The resistors and capacitors are connected in series, meaning that the same current flows through each component.

2. How does a two loop RC circuit work?

In a two loop RC circuit, the capacitors store electrical charge and the resistors regulate the flow of current. When a voltage source is connected to the circuit, the capacitors will charge and discharge according to the voltage and current flowing through the circuit. This results in a changing voltage and current over time.

3. What are the key equations for solving a two loop RC circuit problem?

The key equations for solving a two loop RC circuit problem are Kirchhoff's laws, which state that the sum of the voltage drops around a closed loop must be equal to the voltage sources in that loop, and Ohm's law, which relates the voltage, current, and resistance in a circuit. Additionally, the equations for calculating the time constant, capacitance, and impedance of the circuit may be necessary.

4. What factors affect the behavior of a two loop RC circuit?

The behavior of a two loop RC circuit is affected by the values of the resistors and capacitors, the voltage source, and the frequency of the signal. The time constant, which is determined by the resistance and capacitance values, also plays a significant role in the behavior of the circuit.

5. How can I solve a two loop RC circuit problem?

To solve a two loop RC circuit problem, you can use a variety of methods such as applying Kirchhoff's laws, using circuit analysis techniques, or using simulation software. It is important to carefully analyze the circuit and understand the behavior of each component in order to accurately solve the problem.

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