Question

Circuits ~ Equivalent Resistance

What is the equivalent resistance of this circuit?
(No two resistors have similar resistance.)

Answer 1

\[R_{2} . R_{4} \neq R_{1} . R_{5}\]

Answer 2

Lots of ways to solve. Solutions tend to involve quite a bit of algebra so I won't type it all out, but if any of these methods sound familiar from your class, I'd recommend giving them a shot:
thevenin equivalents using the nodes around R3 as your load
creating 3 mesh currents, one per visible loop, and analysing from there
final option would be to label all the nodes and use kirchoffs laws to determine equations for the relationships between the node voltages and the currents entering and exiting each node

It's not a terribly pretty problem when it's entirely variables. You can look a bit into wheatstone bridges if you're interested in similar circuits. Or I could go through an example with some sample values in the circuit instead if you just want to get more comfortable with the concepts. But I can't say I want to trudge through the algebra right now D:

Answer 3

Or if you'd like a work through of the answer in a much neater form than i'd be able to manage, give this site a look: http://web.clark.edu/ggrey/PHYStext/11Circuits.html

Answer 4

You can also use star delta transformation

if you convert that upper delta to star it will be much easier

Answer 5

Thank you very much @LifeEngineer ,
I was making a question for my students about using Wheatstone bridge in a few University entrance exam tests. I wondered How it could change if it wasn't a Wheatstone bridge. That's why I added that condition in my first answer.

I really don't know how to derive thevenin equivalents. I haven't used them before. And I've used Kirchhoff's laws to find the currents passing each of resistances. How can I use it to find the equivalent resistance here?

Answer 6

I think @rvc 's suggestion is easier for me to use.
@rvc , could you guide me more?

Answer 7

Delta to Star transformation was a great hint.
Just check if i'm correct or not:

Answer 8

Perfect!!!
u r correct
ahead those two branches are parallel...
then in series

Answer 9

But i still like to know how to use thevenin equivalent.
I've got no idea where to start,

Answer 10

first you find the thevinins equivalent Voltage

Answer 11

do you know the steps?

Answer 12

Unfortunately no.
Could you gimme a good URL where things are expplained better than in wikipedia?

Answer 13

hmm..
i need to search

Answer 14

it'd be big kind of u.

Answer 15

i believe this is perfect :
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.html

you can also search other topics from this site

its awesome!

Answer 16

actually, i found openstudy when I was reading an article at hyperphysics.com about the speed of electrons in a wire.
Yes, explanations there are very good. Thank you very much rvc

Answer 17

Lol
thats good

Answer 18

I haven't seen the star delta equivalents before. Thanks for that @rvc , definitely good to know!

Answer 19

my pleasure @LIfeEngineer

Answer 20

hey @Yavar Sir and @rvc you can also solve this kind of problem by using the concept of UNBALANCED WHEATSTONE BRIDGE also

Answer 21

i actually don't know what is STAR DELTA all these stuff !

Answer 22

i can clearly notice that information provided in question simply indicates that circuit provided is UNBALANCED WHEATSTONE BRIDGE !

Answer 23

you can google it also that how to solve UNBALANCED WHEATSTONE BRIDGE problems.
Hence,you will be able to find equivalent resistance !

Answer 24

If you have any problem regarding this,please let me know.
:)
@Yavar Sir and @rvc

Answer 25

there are many ways to solve a particular problem
we pick up that method with which we are comfortable

Answer 26

i know behn.. but since i don't know that conversion method,i preferably use my basic method !

Answer 27

inspite that of, it is not in JEE syllabus though,it is being taught in colleges !

Answer 28

it is not in college level
it is in engineering stuff

Answer 29

lol
in electronics branch naa