Physics - circuits

After S is closed, the left 1-ohm and 2-ohm resistors are in paeallel, the equivalent resistance = 1x2/(1+2) ohms = 2/3 ohms

Similarly, the right 2-ohm and 1-ohm resistors are in parallel, equivalent resistance = 2x1/(2+1) ohms = 2/3 ohms

The total resistance = (2/3+2/3) ohms = 4/3 ohms
hence, main current = 6/(4/3) A = 4.5 A

Current through upper-left 1-ohm resistor = 4.5 x (2/3) A = 3 A
Current through upper-right 2-ohm resistor = 4.5 x (1/3) A = 1.5 A
Thus, a current of (3-1.5) A= 1.5 A is diverted away through XY

Current through lower-left 2-ohm resistor = 4.5 x (1/3) A = 1.5 A
Current through lower-right 1-ohm resistor = 4.5 x (2/3) A = 3 A
Thus, a current of (3-1.5) A = 1.5 A is gained from XY.

Therefore, a current of 1.5 A is flowing from X to Y.

[Although you could get the answer in this way, the question is badly set. There is contradiction anyway. Since X and Y are joined together after S is closed, X and Y should be at the same potential. Hence, it could hardly say that there is a current of 1.5A flowing without a potential difference along XY].

It's a very interesting circuit

2008-10-29 18:16:09 補充：
physics8801 is right in calculation. Main current is 4.5 and the 2 resistors form a current divider. (1/3) means 1/3 of the main current 4.5 goes thru the 2 ohm, and 2/3 of the current goes thru the 1 ohm. You calculate all the currents flow thru each resistor and then you come up with the value of XY and flow direction. Right here, nothing to do with ohm's law.

Sorry, Dr.physics8801, I did all the talking for you. Hope u don't mind.

Besides, There is no contradiction in the circuit set up after I thought about it during my toilet time. No p.d., no current flow is not wrong but misguided here. It's like a child's IQ quiz and teaser for experienced ohm's law guys. Imagine the current flows from one resistor to another resistor in series connected thru a wire. The p.d. across the wire of course equals 0, but the current does flow thru the wire due to the p.d. across the 2 resistors in series. That's why I said misguided because our heads are loaded with only V=IR and cannot see simple things logically. Simple logic is: there is always current flow in the WIRES in a loaded circuit. This is my new theory in electric circuits. ha, ha,ha :)

Don't even think about giving me any points as Dr physics8801 really deserve all the credits.

2008-10-29 18:22:20 補充：
grammar correction: 'deserve' in the last sentence should be deserves. Anybody cares to check grammar for me? For free credit points? I'm a stingy guy. Everybody knows.