R2 = 2 ohm
R3 = 3 ohm
R4 = 4 ohm
R5 = 5 ohm
R6 = 6 ohm

I2 = ?
I3 = ?
I4 = ?
I5 = ?
I6 = ?

Could you please help me solve this Kirchhoff exercise?

Thank all

 

Hi abc.
Welcome to AAC.
Check out this AAC Article, ask if you need assistance.
E
https://www.allaboutcircuits.com/textbook/direct-current/chpt-6/kirchhoffs-current-law-kcl/

also
https://www.allaboutcircuits.com/worksheets/kirchhoffs-laws/

 

I'm already familiar with Kirchhoff's laws—thanks anyway—but I don't know how to solve this particular problem.ericgibbs

 

One method would be to convert R2/R3/R4 from delta to a star network. After that it's much easier to calculate voltage/current across/through R5 and R6. If you have those you can get immediately the voltage/current across/through R2, R3 and finally R4 from the original network.

 

He likely hasn't been exposed to Y-Δ conversions yet.

You have two unknown voltages at the T intersections. Call them Va and Vb.

Then define your currents. I2 is not a current definition as it does not specify direction. Annotate your diagram with the quantities you will be using. The directions you assign to the currents are arbitrary -- flip a coin, if you must. But once you assign a direction, use it consistently throughout the problem.

For instance:



Now you can write each of the currents in terms of the four node voltages and apply KVL and KCL to solve for everything.

Beyond this, you need to show your best attempt to get further assistance.

 

I’ve always been bemused as to why Gustav Kirchhoff was credited with coming up with two “laws” which merely state the blindingly obvious. And then people invent unrealistic circuits for students to solve using his laws.

It’s just a bit of algebra. As already suggested, assume the voltages at the top and bottom of R4 are Va and Vb respectively and write down the current in each resistor according to Georg Ohm’s law. I recall that Gustav mentioned something about the sum of currents into a node are zero, but how could anyone before him think otherwise?

 

I'm not sure either, Jerry-Hat-Trick. I haven't figured out how to solve this problem yet, and no one has taken the time to provide a detailed, step-by-step explanation that I could learn from.

 

And you have not shown your attempt at a solution, as you have been asked. It is easier to help you if we know where you are stuck.

 

Kirchhoff’s laws, if applied directly, create a large matrix to solve. There are shortcuts. Have you learned the node voltage method and the loop current method? These reduce the number of variables and equations.

 

Do as Jerry has suggested. Label the voltages at R4 as Va and Vb.
Write down the equations for the currents in each resistor using Ohm's Law.
Use KCL and arrive at two equations with two unknowns. Solve for Va and Vb.

 

I’ve always been bemused as to why Gustav Kirchhoff was credited with coming up with two “laws” which merely state the blindingly obvious. And then people invent unrealistic circuits for students to solve using his laws.

It’s just a bit of algebra. As already suggested, assume the voltages at the top and bottom of R4 are Va and Vb respectively and write down the current in each resistor according to Georg Ohm’s law. I recall that Gustav mentioned something about the sum of currents into a node are zero, but how could anyone before him think otherwise?

Because they weren't blindingly obvious at the time. Today, we recognize KCL as simply a manifestation of the conservation of charge, but at the time, the theory of electricity was far less settled. Kirchhoff published his laws in 1845 (while a 21 year old student), based on empirical analysis of circuit behavior, as a way of extending Ohm's Law (which was met with great skepticism when it was published less than twenty years earlier) to networks of components. You might ask why it wasn't obvious by just deriving them from Maxwell's equations? Simple. Maxwell's equations weren't published for another twenty years after Kirchhoff's laws. Like Ohm, it took about a decade before the validity of Kirchhoff's Laws were widely accepted.

As for the unrealistic circuits that people invent, those are primarily as a means to get students to practice applying the concepts and working the math, while sticking to the few concepts that they have yet been exposed to. Beginning engineering students have always tended to need strengthening of their algebra skills, and that is far more the case today when so many of them have extremely weak arithmetic skills and virtually non-existent algebra skills.

 

I'm not sure either, Jerry-Hat-Trick. I haven't figured out how to solve this problem yet, and no one has taken the time to provide a detailed, step-by-step explanation that I could learn from.

As I stated, to get further assistance, you need to show your best attempt to work YOUR homework problem. We are not here to do you work for you. So show your work as far as you can take it. Don't worry about whether it is wrong or not. By seeing what you have done wrong, or what you have overlooked, we can help steer you onto the right path.