Calculate Equivalent Resistance of a 5 Resistor Bridge Circuit | Kirchhoff's Loop & Junction Rules

This circuit can NOT be reduced using basic series and parallel reductions. Instead this problem must be solved using loop rule and junction rules.

The physics of this problem is not overly difficult, however the algebra causes most people to get lost in solving the problem. Here we take a look at using Ohm's Law to set up a system of equations that can be used to solve for the current and voltage at each resistor as well as the equivalent resistance of the entire circuit.

Yes you can use a Delta-Y transformation here, but often people encounter this problem before learning that technique.

The topic of Wheatstone Bridges often comes up in introductory physics and engineering courses such as AP Physics C E&M, Electricity and Magnetism, Physics 202, Physics 8.02 and appears on A Level physics as well as the JEE.

[spark-starter]

I was having a bit of trouble grasping the concept of Kirchhoff's rules, so thank you for your explanation! :)

[wf.i.]

Use the D-Y transformation and you solve it in less than 2 lines.

[ralbsphy]

I have a question, in 14:55, where did 1.92 come from for I1? I have already done the previous steps before that, yet I couldn't seem to get the desired answer in the end. Thank you in advance!

[SleepyKirumi]

Omggg thank u soooo much iam in last year in highschool and iam from Egypt and that's helped me a lot tyyy 🥺🥺🥺 wish i could live in America

[balla]

This was extremely helpful even for cementing the basics. I got stuck every time when making my equations but your explanation helped me understand how to start combining them.

[lankog]

That is an absolutely great explanation! Keep up the great work.

[KingJohn-ty]

Why is I3 1.4 instead of 0.147 I did ur calculation in my calculator for I3 and I got 0.147

[taslimaakhter]

WOW! appreciate your efforts. Thank you so much for explaining the way of doing this math.

[scor]

Pls, any practical result out of this except a practice in a simple algebra? The bridge itself is used to measure voltage only between the middle points. And is widely used because any input voltage noise is eliminated and does not affect a measured result.

[shifralacdang]

Thank you for this video! may I ask why I1=1.92 A?

[devababil]

Thank you so much for your wonderful explanation. Take love & respect from Bangladesh....🥰🥰🥰🥰🥰🥰🥰🥰

[themoonwolf]

In 12:38 where did 4I1 and 4I3 came from? More specifically where did that "4" came from? Since I1 and I3 have 1Ω and 3Ω resistors, then what that "4" does there? Is that the substitute of so called 4I4??

[aayushpandey]

I get what you're saying.


"Don't Get What You Are Saying. 😿"

[redbaron]

You can use the online HTML5 "PhET Circuit Construction kit (DC)" to "build" this circuit and check the result. I found that the battery current was 3.098 A to a couple of extra significant figures.

[themoonwolf]

Only question, on rearranging. Why in the first equation the I3 equal to I3=(5I1-9)/4 while for I2 it is equal to I2=(9-5I3)/7? Why isn't it I2=(5I3-9)/7?