AL DC circuit

You need to use Kirchoff's Rules.
Let i1 be the current through the upper branch 2-ohm resistor
i2 be the current through the lower branch 3-ohm resistor
i3 be the current through the 4-ohm resistor (assume going downward from X to Y)

Then, current throug the upper branch 3-ohm resistor = (i1 - i3)
current through the lower branch 2-ohm resistor = (i2 + i3)

Consider the path from the 10 v battery to the upper branch 2-ohm and 3 ohms resistors and back to the battery.
2(i1) + 3(i1 - i3) = 10
i.e. 5(i1) - 3(i3) = 10 -------------------------- (1)

Consider the loop with upper branch 2-ohm, the 4-ohm and lower branch 3-ohm resistors,2(i1) + 4(i3) - 3(i2) = 0 --------------------- (2)

Now, consider the loop with upper branch 3-ohm, the 4-ohm and lower branch 2-ohm resistors,
3(i1 - i3) - 2(i2 + i3) - 4(i3) = 0
i.e. 3(i1) -2(i2) -9(i3) = 0 ------------------------- (3)

You have three unknowns and 3 equations, solve for i1, i2 and i3 gives the following results,
i1 = 2.214 A
i2 = 1.952 A
i3 = 0.357 A
[do check the calculations because there may be truncation error]

Hence, potential difference between X and Y = 4(i3) = 4 x 0.357 v = 1.428 v
i = i1 + i2 = (2.214 + 1.952) A = 4.166 A

多謝Rooney10既回答,但好似唔岩,大概係因為你所用既eq. :
Voltage across the 2 Ohms = 10 X 2 / (2+3) = 4 V,因為呢條formula係限於same current through both resistors,但事實上current through both resistors係唔一樣既
但都多謝你ans

2011-03-05 15:59:12 補充：
天同師兄你係唔係神?
我做果陣let多左野,搞到再唔到,我另外let左i3,i4,係經右上同右下,唔怪得,
想請問師兄你點知 i3 is the current through the 4-ohm resistor from up to down
plx e-mail

1)


圖片參考：http://imgcld.yimg.com/8/n/HA00801958/o/701103040082413873386670.jpg


In a single circuit loop, the sum of voltage across the 2 Ohms resistor and the 3 Ohms resistor must equal to 10 V.
Voltage across the 2 Ohms = 10 X 2 / (2+3) = 4 V
Voltage across the 2 Ohms = 10 - 4 = 6 V
Therefore, the potential difference* between points X and Y is equal to 2 V as shown above.

2) By the Kirchhoff's First Law, at any junction in a circuit, the total current arriving is equal to the total current leaving.


圖片參考：http://imgcld.yimg.com/8/n/HA00801958/o/701103040082413873386671.jpg

At point A, i = I' + I''
I' = 4 / 2 = 2 A
I'' = 6 / 3 = 2 A
Therefore, i = 2 + 2 = 4 A

*1) The potential at a certain point X or Y cannot be determined since the circuit is not earthed. Only the potential difference between any two points can be found.