Simple Circuit Analysis Given Power

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Discussion Overview

The discussion revolves around a hypothetical circuit analysis involving a 12V power source, a 5Ω resistor, and a black box that dissipates 60W of power. Participants explore the implications of these parameters on circuit behavior, focusing on the calculations and theoretical limits of power transfer within the circuit.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) presents a circuit with a 12V source and a 5Ω resistor in series with a black box consuming 60W, expressing confusion over the resulting complex numbers from their calculations.
  • Some participants question how the black box can consume 60W without an alternative energy source, suggesting that it may imply negative energy consumption or energy generation.
  • One participant calculates the maximum power available from the circuit, concluding it to be 7.2W, which raises doubts about the feasibility of the black box's power consumption.
  • Another participant introduces hypothetical ratings for the black box, suggesting that if it has a rated power of 60W and a rated voltage of 12V, it would imply a different resistance and current than initially considered.
  • There is a suggestion that the black box could have an external power supply, which could allow it to draw more power than the circuit alone would provide.
  • Some participants express concern about the nature of the problem and the potential for misinterpretation, suggesting that the OP may need to clarify their initial scenario.

Areas of Agreement / Disagreement

Participants generally agree that the scenario presents inconsistencies regarding power consumption and circuit limitations. Multiple competing views remain regarding the nature of the black box and its power requirements, and the discussion remains unresolved.

Contextual Notes

Participants note limitations in the assumptions made about the black box and the circuit, including the lack of information about the black box's characteristics and the implications of its power consumption exceeding the maximum power available from the circuit.

Who May Find This Useful

This discussion may be of interest to those studying circuit analysis, power transfer in electrical systems, and the implications of hypothetical scenarios in electrical engineering.

elimenohpee182
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Today at work I was thinking hypothetically about a simple circuit that I was unable to get an answer that made any sense. What if you had a simple 12V source with a 5Ω resistor in series, also in series with a black box that consumes 60W of power. You aren't given any characteristics about the black box other than it dissipates 60W. When I do a KVL around the simple loop, I obtained 12V - 5i - 60/i = 0, since P = VI and for this device V and I are both unknown. If I multiply through by i, you can obtain a quadratic formula, but neither of the results physically make sense; in this example they result in complex numbers, and even the magnitude of the real part isn't near what I was expecting.

This was driving me nuts today and it is so simple, but somewhere I am not right. Any ideas?
 
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elimenohpee182 said:
Today at work I was thinking hypothetically about a simple circuit that I was unable to get an answer that made any sense. What if you had a simple 12V source with a 5Ω resistor in series, also in series with a black box that consumes 60W of power. You aren't given any characteristics about the black box other than it dissipates 60W. When I do a KVL around the simple loop, I obtained 12V - 5i - 60/i = 0, since P = VI and for this device V and I are both unknown. If I multiply through by i, you can obtain a quadratic formula, but neither of the results physically make sense; in this example they result in complex numbers, and even the magnitude of the real part isn't near what I was expecting.

This was driving me nuts today and it is so simple, but somewhere I am not right. Any ideas?
The maximum power available from a 12V battery through a 5 ohm resistor will be when the resistor drops half the voltage, then current is 6V / 5R = 1.2 amp.
Wmax to the load is therefore 1.2A * 6V = 7.2 watt.
How can you get 60 watt from the black box if it does not have an alternative supply of energy?
Is it consuming negative energy = generating energy.
 
Baluncore said:
The maximum power available from a 12V battery through a 5 ohm resistor will be when the resistor drops half the voltage, then current is 6V / 5R = 1.2 amp.
Wmax to the load is therefore 1.2A * 6V = 7.2 watt.
How can you get 60 watt from the black box if it does not have an alternative supply of energy?
Is it consuming negative energy = generating energy.

True story.

The black box has an external power supply...maybe like an op amp or something of that nature.

So if you are confused how the 12 volt battery gets that much power to black box...don't be, because it can't with the 5 ohm resistor dicating the story.
 
Indeed as Baluncore said: solution of your 12i-5i^2+60=0 it is i=[12+/-sqrt(144-4*5*W)]/2/5.
This will be a complex number while the black box power is more than 7.2 w[144/4/5].
So 7.2 W it is maximum allowable power for this black box.
 
Perhaps a pause whilst the OP conjuors up a response?? This is clearly a weird problem.
 
I agree with you, sophiecentaur. However, since OP said “I was thinking hypothetically “, we may continue hypothetically.:shy:
Let's say the black box ratings are: Prated=60 W; Vrated=12 V.
Then Rrated=12^2/60=2.4 ohm
Now i=12/(5+2.4)=1.62 A. The power dissipated by black box Pact=2.4*1.62^2=6.3 W
If the black box temperature will be now lower than rated then the black box resistance will be lower.
For 30oC difference the copper will be (1+0.00393*30)=1.12 times less. Ract=2.4/1.12=2.147 ohm. i=12/(5+2.147)=1.68 A; Pact=2.147*1.68^2=6.06 W[!]. :devil:
 
Many threads get launched by a newcomer and then PF 'regulars' get into it and give it 'the treatment' (I include myself here). Sometimes, I think we often read too much into the OP and all that was really necessary may have been to give some clarification - or to point out a possible mistake. Our enthusiasm can scare people off and we don't want that. I was just hoping for a bit of feedback before too much of an avalanche.
 
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Or perhaps you have all been baited?
 

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