Reducing Circuits to Their Simplest Form

In summary, the conversation is discussing a homework problem that involves determining which circuits can be reduced to a single resistor and battery through combinations of resistors in series and parallel. The possible options are A, B, C, D, and E, and the conversation narrows it down to E being the correct answer. The conversation also mentions the delta to Y transformation, but it is ultimately determined to not be necessary for solving the problem.
  • #1
sweetdion
64
0

Homework Statement


Which of the following circuits could be reduced to a single resistance and a battery by determining the equivalent resistance using combinations of resistors in series and parallel?
Screenshot.png


A. II and IV only
B. I and II only
C. II and III only
D. I and III only
E. I and IV only


Homework Equations



Parallel: 1/Req = 1/R1+1/R2+...
Series: Req= R1+R2+...

The Attempt at a Solution



I think 3 and 4 can be eliminated because it seems impossible that you can reduce those to just one resistor.

So I'm thinking the answer is I and II only, but I'm unsure.
 
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  • #2
Take a closer look at 4. Redraw it (hint: it'll have 3 parallel resistor branches).
For 2, are you planning to use the delta to Y transformation?
 
  • #3
Melawrghk said:
Take a closer look at 4. Redraw it (hint: it'll have 3 parallel resistor branches).
For 2, are you planning to use the delta to Y transformation?

I don't even know what you mean by the delta to Y transformation :redface:
 
  • #4
sweetdion said:
I don't even know what you mean by the delta to Y transformation :redface:

Don't worry about it then :) It's a transformation that would allow you to change circuit 2 into battery+resistor circuit. Since you said you thought it could be solved, how did you plan on reducing on?
 
  • #5
well the resistors on the outer edges of the diamond are in series. You can reduce those to one resistor each. Then you have 3 resistors in parallel which you can reduce...i think
 
  • #6
sweetdion said:
well the resistors on the outer edges of the diamond are in series. You can reduce those to one resistor each. Then you have 3 resistors in parallel which you can reduce...i think

For circuit 2? That wouldn't be correct. Every resistor is connected to nodes (point where 3 or more wires meet) at both of its ends. You can only claim that resistors are in series if they do not have a node inbetween them.
---R1----R2---- Resistors 1 and 2 are in series

---R1---R2---- Resistors 1 and 2 are NOT in series
''''''''''''''|
'''''''''''''R3
'''''''''''''|

That is however the correct approach for circuit 4.
 
  • #7
Okay, So I see what your saying. The correct answer would be E. I and IV, unless I've got something wrong out of your explanations...
 

1. What is the purpose of reducing circuits to their simplest form?

The purpose of reducing circuits to their simplest form is to simplify the circuit and make it easier to analyze and understand. This can also help identify any potential errors or inefficiencies in the circuit.

2. How is a circuit reduced to its simplest form?

A circuit can be reduced to its simplest form by using techniques such as series and parallel combinations, Thevenin's and Norton's theorem, and simplification rules such as Ohm's Law and Kirchhoff's Laws.

3. Why is reducing circuits to their simplest form important in circuit design?

Reducing circuits to their simplest form is important in circuit design because it helps to minimize the number of components needed, reduce costs, and improve the overall efficiency and performance of the circuit.

4. Can reducing a circuit to its simplest form affect its functionality?

Yes, reducing a circuit to its simplest form can affect its functionality. In some cases, simplifying a circuit too much can alter its behavior or function, so it is important to carefully analyze the circuit before and after reduction.

5. Are there any limitations to reducing circuits to their simplest form?

Yes, there are limitations to reducing circuits to their simplest form. Some circuits may be too complex to reduce using traditional methods, and specialized software may be needed. Additionally, reducing a circuit to its simplest form may not always result in the most efficient or optimal design.

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