Question

IF a 4 resistor, a 7 resistor, and a 12 resistor are connected in parallel, which has the most current in it?

Answer 1

Do you know how to find the equivalence resistance of parallel resistors?

Answer 2

yes

Answer 3

Okay! If you use \(5\Omega\) resistors, what is the equivalence for 4 resistors, as compared to 12?

You can also take a look at the algebra using \(R\) ohm resistors.

Answer 4

\(\rm\large\color{green}{4~resistors}\)
\(\dfrac1{R_{eq}}=\dfrac1{\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R}\)

vs.
\(\rm\large\color{green}{7~resistors}\)
\(\dfrac1{R_{eq}}=\dfrac1{\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R}\)

So, we're looking at the reciprocal of equivalences. Which reciprocal is greater, and which is lesser?

Answer 5

Hint: which denominator is lesser, and which is greater?

Answer 6

thanks
again

Answer 7

No problem. Do you know the answer and why, yet?

Answer 8

I did some algebra below to show you another way of looking at four resistors:
\(\dfrac1{R_{eq}}=\dfrac1{\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R}=\dfrac1{4\dot\ \dfrac1R}=\dfrac R4\)

Answer 9

not yet but i'll have to look over it later; I'm bout to go to work but u been so much help!!! :)

Answer 10

So...
\(R_{eq}=\dfrac4R\)

You're welcome! Take care!

Answer 11

PFFFTT!!! I Knew I did something wrong.

It's been a while.

\({R_{eq}}=\dfrac1{\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R}=\dfrac1{4\dot\ \dfrac1R}=\dfrac R4\)

Much better....

Answer 12

So.... Doing the same thing to the equivalence resistance for 7,
\({R_{eq}}=\dfrac1{\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R+\dfrac1R}=\dfrac1{\dfrac7R}=\dfrac R7\)

Now you can think, does more resistors RAISE the the resistance?
I'll make a table:
\(\begin{matrix}\rm \#~of~resistors&\quad &\rm equivalence~resistance\\
4&&\rm \dfrac R4\\\\
7&&\dfrac R7\\\\
12&&\dfrac R{12}\end{matrix}\)



What do you do with that?

Well,
\(I=\dfrac VR\)
That's the key.
So, lesser resistance gives you a greater current.
So, how many resistors has the least resistance? That many resistors will have the greatest current.

Answer 13

Boy! It's all the amount of current flows in.

The voltages across the resistors in parallel are same.
So, the product v=ir should be same for all the 3.
Meaning, the one having the least resistance will have the maximum current passing through it.

Answer 14

It is understood by the word, resistance, that it must be something that opposes the flow of charges. More the resistance, more it resists the charges to flow and hence less current.

Answer 15

@Abhishek619
I answered that way because @newtron64 asked a question about how to find series equivalence resistance.

More conceptually, we know that the total voltage across each resistor in parallel is the same. And the current for each is \(I=\dfrac VR\). So, each will have the same current, with equal resistance resistors.
But, where they meet, the current into a junction must be the same as going out. So, if you have more of these resistors, you'll have more currents adding up at the junction.

So, more resistors, more current.

Answer 16

If you increase the resistance, though, there is less current! So you are correct about that, @Abhishek619 . It's just that the question is asking about the number of resistors, here.

Answer 17

:) I have to go. Take care!

Answer 18

Feel free to respond, anybody!

Answer 19

@theEric got the answer!!!! You are great teacher!!!!!!

Answer 20

@theEric Yea sure, I agree with you.
But the point on which I'm stressing on is that the whole calculation can be skipped and this situation can be analysed based on theory alone. That's it.

I apologize if I was harsh on anybody or on anything.

Answer 21

Thanks, @newtron64! Gladd I could help, and sorry I messed up the first try!

No problem @Abhishek619 ! You weren't harsh as I see it! :) I hope I'm not either! And yep, it can be based on theory! Which is good! But it has to be applied right! :)

Answer 22

@theEric Yeah, true. I totally agree with you.

Answer 23

:) Good stuff! :)