A wire structure in the form of a cube has a resistance of one ohm in each edge. An electrical circuit is formed by connecting a one volt battery to a pair of diagonally opposed vertices of the cube. What is the current, in amperes, in the wire connecting the battery to the cube structure?

The 3 resistors connected to the positive battery terminal carry 1/3 of the current and the 6 resistors that are in the middle of the cube will carry 1/6 of the current.
The 6 resistors closest to the battery will have twice the voltage drop and carry twice the current as the middle 6 resistors.
So if the voltage drop across a middle resistor is v, then the total drop across the cube will be 2v + v + 2v = 1 volt or
v=.4 volt and the total current is 3* .4 = 1.2 amps

Posted by JAMES on 2005-05-18 03:05:01