J. Mike Rollins: H

J. Mike Rollins [rollins@wfu.edu]

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Speed of a Piston

H

I frequently run into resistors in an H pattern. I don't know why I've been so unlucky. I finally decided to work out the attributes of this configuration. This is my initial finding.

The parallel and series resistor relations will not solve this configuration. So, I used Kirkoff's law.

I started to work out the equations by hand. The solution was not quickly apparent. I decided to shove these equations into Maple. (I love Maple.)

Here is the maple text:

solve({ V=R1*i1+R3*i3+R5*i5, 
        V=R1*i1+R4*i4,
        V=R2*i2+R5*i5,
        V=R2*i2-R3*i3+R4*i4,
        i0=i1+i2,
        i1=i3+i4,
        i5=i2+i3,
        i6=i4+i5,
        i6=i0}, {i0,i1,i2,i3,i4,i5,i6} );

Executing this with maple gives the following answer. Well, I did not expect the solution to be so complex.

I added these expressions to an XLS file. You can edit the Green fields of the XLS file. I will experimentally test these findings a little later.
Download the XLS file