Construct a 25 ohm resistance from a boz

[cseet]

Hello,

can you advise me how could you construct a 25 ohm resistance from a boz containing a dozen 10 ohm resistors?

can someone explain this in details...
i'm new to physics...

greatly appreciated! thanks again!
cseet

 

[lavalamp]

To work out the resistance of a circuit with some resistors connected in series you simply add their resistances together.

However if you were to connect resistors in parallel then you would have to use this equation:

1  = 1 + 1 + ... + 1
--   --  --        --
R[sub]T[/sub]   R[sub]1[/sub]   R[sub]2[/sub]        R[sub]n[/sub]

So what would the resistance be if you connected two 10 ohm resistors together in parallel?

This should get you most of the way there, let me know if you're still stuck.

 

[lavalamp]

Originally by cseet
"So what would the resistance be if you connected two 10 ohm resistors together in parallel?"

has a 5 ohm resistance... so does it mean that we need 5 sets of (two 10ohm resistors in parallel)? if so, we're using 10 resistor and how would the circuit diagram be?

Just because you have two resistors in parallel, it doesn't mean that you can't have things in series with them, hint hint. ;)

I quoted you in here so that I can be corrected if I'm wrong or if the thread develops and more difficult questions are asked or I'm just too slow then someone else can jump in. Hope you don't mind.

 

[cookiemonster]

No easy way to do it. Just use guess and check.

Resistors in series add like

$$R_\textrm{equiv} = R_1 + R_2 + \cdots$$

whereas resistors in parallel add like

$$R_\textrm{equiv} = (\frac{1}{R_1} + \frac{1}{R_2} + \cdots)^{-1}$$

So build yourself a circuit of resistors and calculate what the resistance is. If it's too high, make some parallel and if it's too low, make some series.

cookiemonster

 

[Chen]

lavalamp already did most of the work... you already know how to connect two resistors to get 5 ohm. You need 25 ohm, i.e you need to come up with a way to connect resistors together so they will together be 20 ohm, and connect that set up to the other set up in series (20 ohm + 5 ohm). How can you get 20 ohm from 10 ohm resistors?

 

[ShawnD]

Don't just guess and check, that's what first graders do.
The trick from the start was finding how to get 5 ohms.

$$R = (\frac{1}{10} + \frac{1}{10} ...)^-^1$$

$$5 = (\frac{n}{10})^-^1$$

$$5 = \frac{10}{n}$$

$$n = 2$$ resistors


Make sure you know how to do that in the future. Guess and check doesn't work too well when you get strange numbers like 341 and it's made of 8 ohm resistors (just an example, it might be impossible).

 

[lavalamp]

Originally posted by ShawnD
Guess and check doesn't work too well when you get strange numbers like 341 and it's made of 8 ohm resistors (just an example, it might be impossible).

Well I look at it and think, how can we get 1 ohm from 8 ohm resistors. Well, use 8 of them in parallel.

Then, how close can you get by using 8 ohm resistors in series, the answer to that is 336 ohms. Plus the 1 ohm from before is 337 ohms, that leaves 4 ohms to go.

To get 4 ohms you can use two 8 ohm resistors in parallel.

So without any guesswork and some simple mental arithmatic the answer is eight 8 ohm resistors in parallel in series with two 8 ohm resistors in parallel in series with forty-two 8 ohm resistors in series.

But point taken, I realize that sometimes it may not be this "easy".