Help with circuits-reactive networks question

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Discussion Overview

The discussion revolves around a homework question related to reactive networks in electrical circuits, focusing on calculations involving energy stored in capacitors, voltage determination in steady-state conditions, time constants, and power calculations. Participants are seeking clarification and validation of their approaches and results.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculated energy stored in a capacitor using the formula \( \frac{1}{2} C V^2 \) and arrived at a voltage of approximately 15.49 volts, but expressed uncertainty about the correctness of this result.
  • Another participant suggested that the first question's answer should be 21.91 volts, indicating a different approach or interpretation of the problem.
  • There was confusion regarding the determination of voltage \( V \) in the second question, with one participant questioning if it is the same as \( V_s \) and discussing the need to treat inductors and capacitors differently in steady-state analysis.
  • One participant reported a calculation of 109.54 volts for the second question by applying the voltage divider equation after simplifying the circuit.
  • For the third question, a participant used the formula \( V = V_0 e^{-t/RC} \) and calculated a time of 0.00957 seconds, questioning if this value was reasonable.
  • Another participant confirmed the use of the power formula \( P = \frac{V^2}{R} \) for the fourth question, but there was a challenge regarding the determination of voltage across a specific resistor.
  • One participant calculated the equivalent resistance of resistors in parallel and series, leading to a time constant calculation, but later realized they had misinterpreted the resistance values as ohms instead of kilo-ohms.
  • Another participant confirmed the power calculation based on the voltage found using the voltage divider formula, but there was still uncertainty about the correctness of the overall approach.

Areas of Agreement / Disagreement

Participants express differing results and approaches to the calculations, indicating that multiple competing views remain on several questions. The discussion does not reach a consensus on the correctness of the various calculations presented.

Contextual Notes

Some calculations depend on the interpretation of circuit components and their configurations, and there are unresolved issues regarding the correct treatment of resistances in kilo-ohms versus ohms. Additionally, the assumptions made in the voltage and power calculations may not be fully aligned among participants.

Davidlong
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Hi guys,

I have this homework question that i have attached. I've done a couple questions but I'm not sure if they are right.



For the first question i arrived at 15.49 by rearranging the formula; energy stored=1/2.C.V^2. when rearranged you get the square root of 240 for voltage.

For the second question b I don't understand how you find V. Is this the same as Vs? OR do you have to find the equivalent circuit by having all the inductors behave as a short circuit and capacitors as an open circuit since the circuit has reached a steady state.

For the third question I think i need the answer from b to continue.

For the fourth question i used the formula of power=V^2/Resistance. So 15.49^2/92 = 2.608mW

Not sure if this is right though.

Any help would be appreciated.

Thanks

 
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Here's the attachment. The first question should be 21.91 using the formula from the last post.
 

Attachments

  • circuit.jpg
    circuit.jpg
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Can you past the actual questions? Can't tell the players without a program.
 
Sorry i uploaded the wrong file.

For the second question i got 109.54 by breaking the circuit down, replacing the capacitors with an open circuit and inductors with a short circuit then using the voltage divider equation.
v0 x (R1+R2/R2) = V.
 

Attachments

  • question.jpg
    question.jpg
    26.1 KB · Views: 355
Davidlong said:
Sorry i uploaded the wrong file.

For the second question i got 109.54 by breaking the circuit down, replacing the capacitors with an open circuit and inductors with a short circuit then using the voltage divider equation.
v0 x (R1+R2/R2) = V.

Yes, that looks reasonable. The result looks okay to me.
 
For the 3rd question i used the formula V=Vo e^(-t/RC) and i got 0.00957 seconds for t. Does this seem correct as its very small.

For the fourth question i used the formula P=V^2/R, 21.91^2/92=5.21739, then i multiplied it by 1000 to give the answer in mW. Did i use the right numbers for this question?
 
Davidlong said:
For the 3rd question i used the formula V=Vo e^(-t/RC) and i got 0.00957 seconds for t. Does this seem correct as its very small.
Show your work. How did you determine the time constant ##\tau = RC##?
For the fourth question i used the formula P=V^2/R, 21.91^2/92=5.21739, then i multiplied it by 1000 to give the answer in mW. Did i use the right numbers for this question?
Nope. How did you determine the voltage across R9?
 
For R i found the equivalent resistant. R8 and R9 in parallel so the resistance when they are combined is 46. Then this new resistor is in series with R7 so they are added together to give 138. C is 0.0001 farads as it says in question 1.

so time constant is 138 x 0.0001=0.0138
0.0138 x ln0.5 = -t = -0.00957.

For question 4 i managed to find the voltage of R9 using the voltage divider formula.

21.91 x 46/92+46 = 7.3 V
46 is the equivalent resistance of R8 and R9.

so for the power i do 7.3^2/92 = 579.71mW

Is that correct?
 
Davidlong said:
For R i found the equivalent resistant. R8 and R9 in parallel so the resistance when they are combined is 46. Then this new resistor is in series with R7 so they are added together to give 138. C is 0.0001 farads as it says in question 1.

so time constant is 138 x 0.0001=0.0138

0.0138 x ln0.5 = -t = -0.00957.
Ah. The resistors are specified in kΩ (kilo ohms), but you've treated them as just ohms. The equivalent resistance should be 1000X what you've used :wink:
[/quote]

For question 4 i managed to find the voltage of R9 using the voltage divider formula.

21.91 x 46/92+46 = 7.3 V
46 is the equivalent resistance of R8 and R9.

so for the power i do 7.3^2/92 = 579.71mW

Is that correct?[/QUOTE]

The power calculation looks okay.
 

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