Equivalent Resistance question HELP

In summary, the conversation is about finding the equivalent resistance between points A and B in an electrical circuit. The equations R_s = R_1 + R_2 + R_n and R_p = (1/R_1 + 1/R_2 + 1/R_n)^-1 are discussed, as well as the concept of series and parallel circuits. The correct answer is determined to be 8 ohms by combining resistors in series and parallel step-by-step.
  • #1
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Equivalent Resistance question HELP!

Homework Statement


The following diagram shows part of an electrical circuit. Find the equivalent resistance between points A and B of the resistor network.

Here is the circuit in question : http://img182.imageshack.us/img182/8742/physicsyf0.th.png [Broken]

Homework Equations


R_s = R_1 + R_2 + R_n
R_p = (1/R_1 + 1/R_2 + 1/R_n)^-1

The Attempt at a Solution


I figured out the equations listed above...we have not discussed this in lecture yet (and the homework is due tomorrow before our recitation so I can't get help) so I tried the best I could by reading the text. Here's what I think...

The 28 ohm, 5 ohm, and 23 ohm resistors are in a series so they can be replaced by a 56 ohm resistor. The same can be said about the 38, 8, and 7 ohm resistors being replaced with a 73 ohm resistor. Now, the 9 ohm, the 73 ohm, and 56 ohm resistors are parallel so using the R_p equation:

R_p = (1/9 + 1/73 + 1/56)^-1 = 7.00 ohms

The correct answer is 8 ohms...what am I doing wrong? Do I not understand the concept of series and parallel circuits correctly? Thanks in advance to anyone who helps.
 
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  • #2
You have the right idea, but as you collapse each combination of resistors into one resstor, keep that one resistance as you do further combinations.

-- combine 28 5 and 23 in series

-- combine that in parallel with 8

-- add that in series with 38 and 27

-- and then what do you do with the 9 Ohms?
 
  • #3
Ah, I see...then the 9 ohm resistor would be parallel to the final resistor...thanks!
 

1. What is equivalent resistance?

Equivalent resistance is the single resistance value that represents the total resistance of a complex circuit.

2. How do you calculate equivalent resistance?

The formula for calculating equivalent resistance depends on the type of circuit. For series circuits, you simply add all the resistances together. For parallel circuits, you use the formula 1/Req = 1/R1 + 1/R2 + 1/R3 +... where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances.

3. Why is equivalent resistance important?

Equivalent resistance helps simplify complex circuits and makes it easier to analyze the behavior of the circuit. It also allows us to calculate the total current and voltage in the circuit.

4. How is equivalent resistance used in real-life applications?

Equivalent resistance is used in various electronic devices and systems, such as in household appliances, cars, and computers. It is also important in designing and troubleshooting electrical circuits in industries and research labs.

5. Can the equivalent resistance of a circuit ever be lower than the individual resistances?

No, the equivalent resistance can never be lower than the lowest individual resistance in a circuit. This is because adding more resistors in parallel will always decrease the overall resistance, and adding more resistors in series will always increase the overall resistance.

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