A Square of Resistors

Find the equivalent resistance between the points A A and B B . All of the Resistors are of 10 Ω 10\Omega .


The answer is 5.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Sravanth C.
Feb 17, 2016

This is a very simple circuit. In particular, it is not the Wheatsone bridge (see note below). We can easily observe the the circuit can be collapsed into a 10 Ω 10\Omega resistor in parallel with two 20 Ω 20\Omega resistors as shown in the figure below:

Thus the equivalent resistance will be: 1 R e q = 1 20 + 1 10 + 1 20 = 1 + 2 + 1 20 = 1 5 R e q = 5 Ω \begin{aligned} \dfrac{1}{R_{eq}}&=\dfrac{1}{20}+\dfrac{1}{10}+\dfrac{1}{20}\\ &=\dfrac{1+2+1}{20}=\dfrac{1}{5}\\ &\therefore R_{eq}=\boxed{5\Omega} \end{aligned}


Note: For those who think that this is the Wheatstone bridge, look at the image carefully. The Wheatstone bridge connects the other 2 set of vertices, like so:

I got 0.2 Ohms, idk why: 0.05 + 0.1 + 0.05 = 0.2 Ohms, im right?, lol, 3deep5me this problem.

Efraín Schrödinger - 5 years, 3 months ago

Log in to reply

You need to reciprocal 0.2

Department 8 - 5 years, 3 months ago

Hey brother don't you think there is a Wheatstone bridge forming. So I believe the answer is 10, please correct me if I am wrong

Department 8 - 5 years, 3 months ago

Log in to reply

Well can you explain your steps?

Sravanth C. - 5 years, 3 months ago

Log in to reply

Dude I got the answer right but we know there is a Wheatstone Bridge only if A/B=C/D. If you have HC Verma 2, check in the chapter Electric Current in conductors, (page 181)

Department 8 - 5 years, 3 months ago

Log in to reply

@Department 8 the wheatstone bridge is totally different .. the terminals of the resistors for which the supposed resistor with no current is not directly attached but attached between the combination

Jaswinder Singh - 5 years, 3 months ago

Log in to reply

@Jaswinder Singh Thanks for that explanation!+1! ¨ \ddot\smile

Sravanth C. - 5 years, 3 months ago

Log in to reply

@Sravanth C. 1 factorial? lol

Ashish Menon - 5 years, 3 months ago

@Jaswinder Singh Oh! Never knew of that thanks.

Department 8 - 5 years, 3 months ago

This is wrong weet stone bridge mid resistor will not work and=10 will be the answer

Rahul Malhotra - 5 years, 3 months ago

Why it is not wheat stone bridge. Give me concrete reason

Hari Om Sharma - 5 years, 3 months ago

Log in to reply

Ok, wait see the following figure:

In this case, there is a Wheatstone bridge and the current won't flow through R 3 R_3 (assuming that this is a balanced bridge). I hope you get it.

Sravanth C. - 5 years, 3 months ago

Because we are not in the context of a wheatstone bridge. It is a simple case of resistors in parallel. It is drawn to resemble the wheatstone bridge, and likely tricked those who did not observe it carefully.

Calvin Lin Staff - 5 years, 3 months ago

Log in to reply

Thanks sir, and if you were the person who changed the image, thanks again! ¨ \ddot\smile

Sravanth C. - 5 years, 3 months ago

Must see to that the figure given satisfies the condition of WHEAT STONE BRIDGE. hence the current wont pass through the mid resistor. and the upper and lower give resistance of 20 ohms each and that too in parallel and this gives the equivalent resistance as 10.

A Former Brilliant Member - 5 years, 3 months ago

Log in to reply

Sorry, but it does not form a Wheatstone bridge, it just appears so.

Sravanth C. - 5 years, 3 months ago

Log in to reply

plz can u explain me the reason for that?

A Former Brilliant Member - 5 years, 3 months ago

Log in to reply

@A Former Brilliant Member It is just a question to trick us. Those who observe it very very carefully, get wrong answers. It is just a case where resistors are parallel to each other

Ashish Menon - 5 years, 3 months ago

@A Former Brilliant Member Ok, wait see the following figure:

In this case, there is a Wheatstone bridge and the current won't flow through R 3 R_3 (assuming that this is a balanced bridge). I hope you get it.

Sravanth C. - 5 years, 3 months ago

Log in to reply

@Sravanth C. ok thnk u. i got it

A Former Brilliant Member - 5 years, 3 months ago

Log in to reply

@A Former Brilliant Member Thanks okay, hope you enjoyed the problem! ¨ \ddot\smile

Sravanth C. - 5 years, 3 months ago

In this it is WHEATSTONE NETWORK current would not flow through 20 phm resistor

Harshit Sahani - 5 years, 3 months ago

The resistor symbols in this circuit indicate that they are all short circuited; Therefore answer should technically be 0.

Thanks. I have fixed the image.

Calvin Lin Staff - 5 years, 3 months ago

Well, nice observation.

Rishik Jain - 5 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...