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標題:
AL DC circuit
發問:
圖片參考：http://imgcld.yimg.com/8/n/HA00270495/o/701103040082413873386660.jpg 我大概是基礎概念不夠好,唔識處理resistance 複雜結構,請師兄指教 1) potential at x and y 2) value of i 請列出運算過程,盡可能以高考範圍作回答步驟!!多謝
最佳解答:
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
其他解答:
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.A9A39959EDCC7BE3
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