Simple (?) EE Question

[klund at MIT.EDU]

> More generally, if you have a star of resistors R1....Rn connected to
> voltages V1....Vn, is there a general formula for the voltage at the
> middle of the star?

Sure, call the middle voltage Vm.  Kircoff's Current Law says that the
total current out of the node must be zero, so:

(Vm-V1)/R1 + (Vm-V2)/R2 + (Vm-V3)/R3 + (Vm-V4)/R4 + ... = 0

putting all the Vm terms on one side, and everything else on the other:

Vm/R1 + Vm/R2 + Vm/R3 + ... = V1/R1 + V2/R2 + V3/R3 + ...

and solving for Vm (by dividing by 1/R1 + 1/R2 + 1/R3 + ...):

Vm = (V1/R1 + V2/R2 + V3/R3 + ...) / (1/R1 + 1/R2 + 1/R3 + ...)

or, more mathematically

Vm = [ SUM_i Vi/Ri ] / [ SUM_j 1/Rj ]

of course, any of the Vi's can be zero, for a connection to ground.

Woo hoo!  Putting that degree to work (and Dad said I never would).

--> Kent.