Parallel and Series Resistor Simplification

In summary, the individual resistors in the circuit can be simplified using the equations for series and parallel resistors. However, there is a point in the simplification process where the remaining 3 resistors are connected by 1 node. To solve this, the 30 ohm resistor should be removed from the network. This will result in the correct answer of 15 ohms for 'R'.
  • #1
nlm
3
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Hi,

I need help simplifying this circuit with parallel and series resistors. I am mainly confused, because there seems to be a point in my simplification where in picture 4 and 5 of my second image where the remaining 3 resistors are connected by 1 node.

I tried to simplify them as resistors in parallel, but I end up with the wrong answer, and this doesn't seem like the correct thing to do.

Homework Statement



The Resistor equivalent of the entire circuit is 9 ohms. And the answer for 'R' is 15 ohms. However I do not know how to obtain this answer.

Homework Equations



Series Resistors = R1 + R2 = Rtotal
Parallel = R2*R1/R1+R2 = Rtotal
= 1/R3 + 1/R2 + 1/R1 = Rtotal

The Attempt at a Solution



Here are the images of my attempted solutions:

image 1 (the problem):
http://img22.imageshack.us/img22/9206/resistor1.jpg

image 2 (my analysis):
http://img22.imageshack.us/img22/4978/resistor2.jpg


Any help would be appreciated.
 
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  • #2
the 30ohm resistor is shorted so just remove it from the network and u'll get the right answer.
 
  • #3
Yes, thank you.

I actually figured it out before the forum posted my question.
 

1. What is the difference between parallel and series resistors?

Parallel resistors are connected side by side, while series resistors are connected end to end. This affects the way current flows through the circuit and the overall resistance of the circuit.

2. How do I simplify a circuit with parallel and series resistors?

To simplify a circuit with parallel and series resistors, you can use the rules for combining resistors in each type of circuit. For parallel resistors, you can use the equation 1/Rtotal = 1/R1 + 1/R2 + 1/R3... For series resistors, you can simply add up the individual resistances to find the total resistance.

3. Can I combine parallel and series resistors?

Yes, it is possible to have a circuit with both parallel and series resistors. In this case, you can simplify the circuit by first combining the parallel resistors using the formula mentioned above, and then adding the resulting resistance to the series resistors to find the total resistance.

4. What happens to the overall resistance when resistors are connected in parallel?

The overall resistance decreases when resistors are connected in parallel. This is because the current has multiple pathways to follow, making it easier for the current to flow through the circuit.

5. How do I calculate the total resistance in a parallel and series circuit?

The total resistance in a parallel circuit can be calculated using the formula 1/Rtotal = 1/R1 + 1/R2 + 1/R3... In a series circuit, the total resistance is simply the sum of the individual resistances. Once you have calculated the individual resistances, you can add them together to find the total resistance of the circuit.

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