What is the formula for solving a network with junction and loop rules?

In summary: I4 + 23I2 = 6I3you can't really "calculate" simultaneous equations, you just solve them using algebrathe idea is to get all the unknowns on one side of the equals sign, and all the knowns on the other side, so you can solve for the unknowns :wink:I am stuck at this point since yesterday.. I even don't know what to substituteI2 from the second equation = I4 - 5I6substitute that into the fourth equationthen put the result into the third equationyou should be able to rearrange that to get a value for I4 and
  • #1
4real4sure
26
0
For the network shown, show that the resistance Rab = (27/17)ohms .

http://www.webassign.net/pse/p28-28.gif
Figure P28.28
My attempt to the problem:
I got the first following equations:
I1-I3-I2=0
I4+I6-I1=0
I2+I5-I6=0
I3-I4-I5=0

Note that I3 and I4 are currents flowing at the top
I2 and I6 are flowing through 3 and 5 ohm resistances
I1 is connected to a battery at tyhe left side of I2
Any help will be highly highly appreciated!
 
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  • #2
welcome to pf!

hi 4real4sure! welcome to pf! :smile:

(hae an omega: Ω and try using the X2 icon just above the Reply box :wink:)

what are your equations involving the amounts of the resistances? :smile:
 
  • #3
they are :
10-I3-I4=0
-I3-I5+3I2=0
-I4+5I6+I5=0
10-3I2-5I6=0

I am just not sure about these equations... Please can you check them out and give your precious precious advice.
 
  • #4
hi 4real4sure! :wink:
4real4sure said:
I1-I3-I2=0
I4+I6-I1=0
I2+I5-I6=0
I3-I4-I5=0

yes, these are fine (except you don't need I1)

but will be easier to use them if we summarise them as:

I2 + I3 = I4 + I6

I6 - I2 = I5 = I3 - I4
4real4sure said:
10-I3-I4=0
-I3-I5+3I2=0
-I4+5I6+I5=0
10-3I2-5I6=0

no, you can't have loop equations involving I1, because you don't know the voltage supplied

you can only have loop equations for the two loops in the diagram

(actually there are three loops, the left one, the right one, and the joint one, but there's only two independent loop equations)

so the correct ones are the second and third one …

I3 + I5 = 3I2

I4 = I5 + 5I6

carry on from there :smile:
 
  • #5
Thank you so much! But whne I am trying to find the values of the current the first three are giving me a weird value which equals infinity..
 
  • #6
show us :smile:
 
  • #7
4real4sure said:
Actually when I am finding the values of the current using MATLAB I am getting
NaN
NaN
NaN
0
0

then don't use MATLAB :wink:

do it yourself! :smile:
 
  • #8
can you kindly check your inbox please
 
  • #9
I don't think its possible without using any tool... I have tried
 
  • #10
substitute from one of the loop equations into one of the junction equations …

what do you get?​

(and please reply on the forum, not by pm :frown:)
 
  • #11
Okay but I ma confused about one thing.. I am not using emf here when I am actually supposed to use it in loop rule
 
  • #12
ah, you only have to use emf if there's an emf in the loop :smile:

lots of loops have no emf …

(in fact, we often prefer loops with no emf, since they're simpler to calculate!)

it's nothing to worry about! :wink:
 
  • #13
That doesn't make sense because if I have no voltage then my current should be zero.
How can you have current with no emf
 
  • #14
take the left loop …

from the left end to the bottom right, there are two ways to go …

diagonally down, or right and then down …

there's no emf in that loop, but current is still flowing along both paths because of the potential difference between the two points …

what https://www.physicsforums.com/library.php?do=view_item&itemid=93" say for that circuit is that the sum of the potential differences is zero if you go round the same way, ie if you go out along one path and back along the other path …

(and that's the same as saying that if you go out along one path, the potential difference is the same as if you go out along the other path! :wink:)
 
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  • #15
Okay honestly, I am completely stumped by the algebra of those five equations.. I am trying since yesterday and I am getting more and more confused while substituting
 
  • #16
4real4sure said:
Okay honestly, I am completely stumped by the algebra of those five equations..

which five equations?

can you please set them out again, so we can be sure they're the right equations :wink:
 
  • #17
Here they are:
I3 + I5 = 3I2
I4 = I5 + 5I6
I2 + I3 = I4 + I6
I6 - I2 = I5
I3 - I4 = 15
 
  • #18
ok

first, you can ignore the fifth equation because it equals the difference between the third and fourth equations

now take I5 from the fourth equation, and substitute it into the first two equations :wink:
 
  • #19
Okay now I have a new equation... 3I2 = I4+I3... don't we have any new software for calculating this type of simultaneous equation
 
  • #20
my fault.. its 23I2 = I4+6I3
 

1. What is the junction rule?

The junction rule, also known as Kirchhoff's current law, states that the sum of all currents entering a junction in a circuit must equal the sum of all currents leaving that junction. This is based on the principle of conservation of charge.

2. How is the junction rule applied in a circuit?

In order to apply the junction rule in a circuit, you must first identify all the junctions in the circuit. Then, you can use the rule to write an equation for each junction, setting the sum of all incoming currents equal to the sum of all outgoing currents. This allows you to solve for any unknown currents in the circuit.

3. What is the loop rule?

The loop rule, also known as Kirchhoff's voltage law, states that the sum of all voltage drops in a closed loop must equal the sum of all voltage rises in that loop. This is based on the principle of conservation of energy.

4. How is the loop rule applied in a circuit?

To apply the loop rule, you must first identify all the loops in the circuit. Then, you can use the rule to write an equation for each loop, setting the sum of all voltage drops equal to the sum of all voltage rises. This allows you to solve for any unknown voltages in the circuit.

5. What is the difference between the junction rule and the loop rule?

The junction rule deals with the conservation of charge, while the loop rule deals with the conservation of energy. The junction rule applies to junctions in a circuit, while the loop rule applies to closed loops. Both rules are based on the fundamental principles of physics and are essential for analyzing complex circuits.

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