3 resistors in parallel: how to get there

In summary, my professor explained that the circuit is equivalent to a circuit with three resistors in parallel, and that the resistance is the parallel of the 3 resistances.
  • #1
Granger
168
7

Homework Statement


2. Homework Equations [/B]

Hi! So I was given the following circuit with R=15k

ATTACH]
Ypbs6Ki.png


I was asked to calculate the equivalent resistance between A and B.

The Attempt at a Solution


[/B]
According to my professor this circuit is equivalent to a circuit with three resistors in parallel, so the resistance is the parallel of the 3 resistances R (= 5k).

However I don't understand how it is equivalent.

My professor explanation was that no matter what pad we choose for a current it will pass only through a resistor (which I totally understand why!). However I don't see how that means mathematically that they are in parallel. Can someone help me clarify it?.

Thanks!
 
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  • #2
The easiest way for me on this problem is to re-draw the circuit. Start with A at the top and B at the bottom, and label the resistors in the original figure R1, R2, R3 from left-to-right. Then you can see that R1 and R2 are in parallel going from A at the top to B at the bottom. Do you now see where R3 goes?
 
  • #3
berkeman said:
The easiest way for me on this problem is to re-draw the circuit. Start with A at the top and B at the bottom, and label the resistors in the original figure R1, R2, R3 from left-to-right. Then you can see that R1 and R2 are in parallel going from A at the top to B at the bottom. Do you now see where R3 goes?

Starting with A we go through R1 and then the circuit parts into R2 and a short circuit (so R1 and R2 are in parallel). After that we have B and R3 (so R1 and R3 are in parallel). Then after R2, we have the same situation (R2 and R3 in parallel).

So if R1 and R2 are in parallel, R2 and R3 and then R1 and R3 then the 3 resistors are in parallel?
 
  • #4
Granger said:
So if R1 and R2 are in parallel, R2 and R3 and then R1 and R3 then the 3 resistors are in parallel?
Yes, but I didn't follow your description, sorry. Start by "pulling" A up to the top of the circuit, which pulls the left of R1 up and the right end of R2 up toward A. Do you see how you can do this because those two ends of R1 and R2 are shorted together by the wire? Then do similar things rotating the rest of the circuit...
 
  • #5
berkeman said:
Yes, but I didn't follow your description, sorry. Start by "pulling" A up to the top of the circuit, which pulls the left of R1 up and the right end of R2 up toward A. Do you see how you can do this because those two ends of R1 and R2 are shorted together by the wire? Then do similar things rotating the rest of the circuit...

Oh I finally got it! Thank you very much !
 
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  • #6
Just FYI, that circuit has appeared here on PF numerous times. It is a standard problem to make sure students really understand series/parallel concepts and that they can redraw a circuit to make things more clear.
 

1. What does it mean for resistors to be in parallel?

When resistors are connected in parallel, it means that they are all connected to the same two points in the circuit, with each resistor having its own individual path for current to flow through. This results in the same voltage being applied to each resistor, but the total current is divided between them.

2. How do I calculate the total resistance of three resistors in parallel?

The formula for calculating total resistance in a parallel circuit is 1/Rtotal = 1/R1 + 1/R2 + 1/R3. So for three resistors in parallel, you would add the reciprocals of each resistor's resistance and then take the reciprocal of that sum. For example, if the resistances are 10 ohms, 20 ohms, and 30 ohms, the total resistance would be 1/10 + 1/20 + 1/30 = 0.1667 ohms.

3. How do I find the current in each resistor in a parallel circuit?

The current in each resistor can be found by using Ohm's Law, which states that current (I) equals voltage (V) divided by resistance (R). So for each resistor, you would use the same voltage value and divide it by the individual resistance. For example, if the voltage is 12 volts and the resistances are 10 ohms, 20 ohms, and 30 ohms, the currents would be 12/10 = 1.2 amps, 12/20 = 0.6 amps, and 12/30 = 0.4 amps.

4. What is the purpose of connecting resistors in parallel?

Connecting resistors in parallel can be useful for a few reasons. It can reduce the total resistance in a circuit, which can allow for more current to flow. It can also help distribute the load among multiple resistors, which can prevent overheating and potential damage to the resistors. Additionally, it can allow for different values of resistance to be used in a circuit while still maintaining the same voltage across each resistor.

5. How do I physically connect three resistors in parallel?

To connect three resistors in parallel, you would need to connect one end of each resistor to the same point in the circuit (such as the positive terminal of a battery), and then connect the other ends of the resistors to the same point (such as the negative terminal of the battery). This ensures that each resistor has its own individual path for current to flow through.

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