How to make total resistance of 1 ohm?

In summary, the equation for parallel circuit is: 1/R1+1/R2=1/R. The equation for serial circuit is: R1+R2=R. The equation for a circuit with one resistor is: R=R1+R2. The equation for a circuit with two resistors is: R1+R2=1/R. The equation for a circuit with three resistors is: R1+R2=1/R1+1/R2. The equation for a circuit with four resistors is: R1+R2=1/R1+1/R2+1/R3. The equation for a circuit with five resistors is:
  • #1
Abs321
4
0

Homework Statement



We have 1Ω, 2Ω, 2Ω, 4Ω, 5Ω and 6Ω resistors. We have to make a circuit with all of them and total resistance must be 1 ohm.

Homework Equations


Parallel: 1/R1+1/R2=1/R
In series: R1+R2=R

The Attempt at a Solution


I have only made a circuit from 4 resistors:
1 ohm and 2 ohms in series, 6 ohms parallel to them and 2 ohms parallel to them all
 
Physics news on Phys.org
  • #2
Hi Abs, :welcome:

Unfortunately, that doesn't count as an attempt (more like an arbitrary guess).
You need a bit more than that; considerations, for example. Like:
Your last step will be a parallel circuit (because a series will exceed 1 ##\Omega##).
That parallel circuit will have ##\ge## two sub-circuits, etc. etc.
Fortunately, I don't have the answer either. :smile: so you must take the first next step

[edit] With a little trial and error I stumbled on the (or: a ) solution. How far are you ?
 
Last edited:
  • #3
Oh, I suppose there could be two parallel circuit from 2 ohms and another sub-circuit totally of 2 ohms and so on, I understand how these laws work, but I can't construct such circuit. Just playing on with resistors.
 
  • #4
Yes, one of the considerations is: the 1 ##\Omega## can't be a single parallel branch (total would go under 1 ##\Omega##).

So the first candidate as a parallel branch would be the 2 ##\Omega##. That reduces the problem to making another 2 ##\Omega## with the remaining 5 resistors (1,1,4,5,6) (since 2 ##\Omega\, \parallel \, 2 \Omega = 1 \Omega ## )

And so on. You're almost there :rolleyes: !
 
  • #5
And this is where I stop. Is it possible to combine 2 ohms in 2 parallel branches from remaining 5 resistors? Or do we need 3 branches?
 
  • #6
Yes. So in total you end up with three branches: one of 2 ohm.
The remainder needs to be 2 ohm. Can't be one branch (I think -- why not ?) but two branches is worth investigating
[edit] turns out to be mistaken. See below .
 
Last edited:
  • #7
Oh, I've just found an answer. It's (6 ∥ 5+1∥ 4+2) ∥ 2
Was your solution simpler?
 
  • #8
Brilliant ! Well done.

My solution was for the wrong problem (1,1,2,4,5,6) o:) instead of (1,2,2,4,5,6). Want to try that too ?
 
  • Like
Likes Greg Bernhardt

Related to How to make total resistance of 1 ohm?

1. How do I calculate total resistance of a circuit?

The total resistance of a circuit can be calculated by adding up the individual resistances in the circuit. This can be done using Ohm's Law (R = V/I) or by using the formula for resistors in series (R = R1 + R2 + R3...).

2. What is the unit of measurement for resistance?

The unit of measurement for resistance is the ohm (Ω), which is represented by the Greek letter omega.

3. Can I make a circuit with a total resistance of 1 ohm using only one resistor?

Yes, it is possible to make a circuit with a total resistance of 1 ohm using only one resistor. However, the resistor must have a resistance of 1 ohm or be adjustable to a resistance of 1 ohm.

4. Can I change the total resistance of a circuit?

Yes, the total resistance of a circuit can be changed by adding or removing resistors or by adjusting the resistance of existing resistors. Additionally, the length and thickness of the wires in the circuit can also affect the total resistance.

5. Why is it important to have a total resistance of 1 ohm in a circuit?

Having a total resistance of 1 ohm in a circuit allows for a predictable flow of current. It also allows for easier calculations when using Ohm's Law to determine voltage and current in the circuit. Additionally, it is a commonly used value for testing and calibrating electronic equipment and components.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
646
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
653
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
19
Views
6K
  • Introductory Physics Homework Help
Replies
18
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top