Resistor Network: Find the Equivalent Resistance Across AB

In summary, the resistor network shown in the figure has an equivalent resistance of 2 ohms. If you were to remove all of the resistors except for the 2 ohm resistor, the net resistance would be the same.
  • #1
lingling
22
0
A resistor network is built up indefinitely as shown in the figure. The equivalent resistance across AB is
A. 1 ohm
B. 1.24 ohm
C. 2 ohm
D. unable to be determined.

-> I don't know where to start with. Can anyone give me some hints?
 

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  • #2
Am I missing something? It looks to me like the picture says that the resistance across AB is 2 ohms. The rest of the circuit is irrelevant.
 
  • #3
HallsofIvy said:
Am I missing something? It looks to me like the picture says that the resistance across AB is 2 ohms. The rest of the circuit is irrelevant.
If you put one end of a battery at A and the other end at B, current will flow not just across the 2ohm resistor you speak of but all the other resistors aswell.

A quick calculation indicates the following.

The resistance for a network of length 1 is 4/3 ohms since 1/(1/2+1/4)=1/(3/4)=4/3

The next value obtained by extending the network by an extra 3 resistors is can be found by again just using the rules for parallel and series resistors. I found this to be equal to 5/4 ohms.

Hence the trend appears to be

4/3
5/4

I would be extremely surprised if this trend did not continue and the next value would be 6/5. In that case if the network is infinitely long the resistance would tend to 1ohm
 
  • #4
But the answer is 1.24 ohm.
I can't understand. Why it is not 2 ohm...?
 
  • #5
Interesting question...

Assume that the total resistance is R. The resistor network right-of (and including) the second 2ohm resistor from the left is exactly the same as the entire resistor network. Thus, we have
R = 2 || (2+R)
Solving for R gives you the desired answer.
 
  • #6
I still cannot understand.
Is there any simpler approach?
 
  • #7
lingling said:
I still cannot understand.
Is there any simpler approach?
doodle has the answer. There is no easier way. There is no end to the chain of resistors, and if you think about how the current will flow you will realize that each 2-ohm resistor will have less current than the previous 2-ohm resistor. If you removed all the resistors touching points A and B, you would have exactly the same net resistance you have with them there.

This problem is a precursor to the important concept of characteristic impedence of transmission lines.

http://www.allaboutcircuits.com/vol_2/chpt_13/3.html
 

Related to Resistor Network: Find the Equivalent Resistance Across AB

What is a resistor network?

A resistor network is a circuit made up of multiple resistors connected in a specific pattern. It is used to control the flow of electric current and can be found in various electronic devices.

Why is it important to find the equivalent resistance across AB?

Finding the equivalent resistance across AB allows us to simplify the circuit and calculate the overall resistance of the network. This is crucial in understanding the behavior of the circuit and making accurate predictions.

How is the equivalent resistance across AB calculated?

The equivalent resistance across AB is calculated using the parallel and series resistance formulas, depending on the arrangement of the resistors in the network. The parallel formula is used for resistors connected side by side, while the series formula is used for resistors connected end to end.

What factors affect the equivalent resistance of a resistor network?

The equivalent resistance of a resistor network is affected by the number and arrangement of resistors, as well as the values of each resistor. Changing any of these factors will result in a different equivalent resistance.

What are some practical applications of resistor networks?

Resistor networks are used in a wide range of electronic devices, such as computers, televisions, and cell phones. They are also used in electrical systems to regulate current flow and protect components from damage.

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