How to find the equivalent resistance of this electric circuit?

In summary: However, I cannot find any reference to equivalent resistance for a circuit with R5 and R6. I suspect that you are misunderstanding something in the text.In summary, the electric circuit has six resistances and the equivalent resistance is 66.6 Ohms.
  • #1
Leonid92
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Summary: How to find equivalent resistance of the electric circuit?

I need to solve the following problem:
Calculate equivalent resistance of the circuit (figure1), if all six resistances are the same: r1 = r2 = r3 = r4 = r5 = r6 = 100 Ohm.
True answer: 66.6 Ohm.

I tried to solve this problem, but I obtained wrong answer. Initially, I suppose that current will not flow to r5 and r6, since there is a wire without any resistor, and therefore the current will flow to where there is no resistance. Thus I consider that r5 and r6 are absent (see figure2 and figure3). After that, equivalent scheme looks like in figure4.
r1 and r2 are connected in parallel, and r3 and r4 are connected in parallel. Total resistance:
r = r12 + r34 = (r1*r2)/(r1+r2) + (r3*r4)/(r3+r4) = (100*100)/(100+100) + (100*100)/(100+100) = 100 Ohm.
Could you please write, how should I calculate equivalent resistance of given circuit?
 

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  • #2
You are correct to assert that R4 and R5 (<-- look! a typo! EDIT: I meant R5, R6) are superfluous. What makes you think that the "true answer" is 66.6 Ohms?
 
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  • #3
lewando said:
You are correct to assert that R4 and R5 are superfluous. What makes you think that the "true answer" is 66.6 Ohms?

The true answer is given in problems section for specific chapter of the electrical engineering textbook (The chapter is called "Simple DC electrical circuits"). It is old textbook published in 1989, and there are some mistakes in it, but I thought that the answer given in this book for the problem that I posted is unlikely to be wrong.
 
  • #4
Mistakes in textbooks can be very frustrating. If you find 2 or 3, then soon everything is cast in doubt (as it probably should be). It forces you to do several things: trust your methods (which are hopefully correct), try alternate methods, look at other textbooks (or internet resources) for confirmation of a suspicion, and probably most importantly, develop a strong foundation in the subject matter.

By the way, I am operating in bufoon mode today. I was trying to edit post #2 to correct an irony-laden typo-- not R4, R5, but rather R5, R6. I killed the post instead. I suppose as humans, we are constrained by our humanity.
 
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  • #5
lewando said:
Mistakes in textbooks can be very frustrating. If you find 2 or 3, then soon everything is cast in doubt (as it probably should be). It forces you to do several things: trust your methods (which are hopefully correct), try alternate methods, look at other textbooks (or internet resources) for confirmation of a suspicion, and probably most importantly, develop a strong foundation in the subject matter.

By the way, I am operating in bufoon mode today. I was trying to edit post #2 to correct an irony-laden typo-- not R4, R5, but rather R5, R6. I killed the post instead. I suppose as humans, we are constrained by our humanity.

I understood that there was typo in post #2 :)
Thank you for your reply!
 
  • #6
Leonid92 said:
100 Ohm.
Your sequence of simplifications looks right.
 
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Related to How to find the equivalent resistance of this electric circuit?

1. What is the definition of equivalent resistance?

The equivalent resistance of an electric circuit is the total resistance that a single resistor would need to have in order to produce the same amount of current as the original circuit.

2. How do you calculate equivalent resistance in a series circuit?

In a series circuit, the equivalent resistance is equal to the sum of all the individual resistances in the circuit. This can be calculated using the formula: Req = R1 + R2 + R3 + ...

3. What is the formula for calculating equivalent resistance in a parallel circuit?

In a parallel circuit, the equivalent resistance is calculated using the formula: 1/Req = 1/R1 + 1/R2 + 1/R3 + ...

4. How do you handle complex circuits with both series and parallel components?

In complex circuits, it is important to break the circuit down into smaller parts and calculate the equivalent resistance for each part separately. These equivalent resistances can then be combined using the appropriate formula for series or parallel circuits.

5. What factors can affect the equivalent resistance of a circuit?

The equivalent resistance of a circuit can be affected by the number and type of resistors in the circuit, as well as the arrangement of these resistors (whether they are in series or parallel). Changes in temperature and material properties can also impact the overall resistance of a circuit.

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