Applications of Linear Systems: Electrical Networks

[adc85]

Hey,

How do I find the current through the central resistor (the one that is 1 ohm) in this Wheatstone bridge attached to this post? What approach do I need to take here if I were to solve this using linear systems? Our professor poorly explained how electrical networks work. I can solve the linear system once I get it but I just need to figure out what I'm supposed to do in order to find those equations. Thanks.

 

[clive]

You must learn to write the Kirchoff's laws for a given electrical network.

http://cnx.rice.edu/content/m0015/latest/

 

[christinono]

Try and redraw the circuit, but simplified so it's easier to see all the "routes" the current can go through. That really helps.

 

[clive]

Another way, without using the Kirchoff's laws, would consist of using the star-triangle transformations and compute in this way the electric potentials at the ends of the central resistor using only the Ohm's laws.

 

[adc85]

See that's the thing, he never drew any arrows in the problem. I think he said something like we can make up our own directions but I really couldn't understand him. Would the final answer be the same no matter what the directions were?

 

[Gamma]

You can choose your own direction. If you have chosen your arrow in the 'wrong' direction, final answer will reflact that. In other words, you will get a negative result.

 

[adc85]

OK here's a revised drawing of the diagram. I labeled the direction of the current this time. Are these directions fine? I know next to nothing about how current, voltage, and resistance work.

 

[Gamma]

Now mark the currents with some notations, say I, i, $$i_1$$.

Say the current through the battory is I.

So at the $$2 \Omega, 3\Omega$$ junction (left side in your recent picture) , let the current through $$3\Omega$$ is i and current through $$2\Omega$$ is I-i (Point rule).

Do similarly at the 3,1,2 junction (top), assuming the current through $$1\Omega$$ is $$i_1$$. Complete the current flow diagram by writing the currents through the other resistors. Don't introduce any other variables.

You need only three variables namely I, i, $$i_1$$. Apply Kirchoff's laws to get three equations to solve.

Some one will be along with you if there is another easy way to do this.

regards,