DC circuit

[匿名]

2013-02-28 3:03 pm

Consider the DC circuit shown in the gure below.

_______R1=1 K omaga __a.______V2=6V_____b_________R2=3K omaga____
|..................................... |..............................|............................................|
| ................................... |...............................|........................................... |
V1= 10V...................... R3=3K omaga ............R4 =4K omaga ..............V3=15V
|....................................|.................................|.......................................... |
|....................................|..................................|......................................... |
|____________________|__________________|________________________|___................................................|
...................................------
................................. ////////

a) What is the current Ii through each of the resistors Ri, i = {1 ; ; 4}? Give both magnitude (in mA) and direction (i.e. ---> or<--- for R1;2 and " arrow top or arrow down for R3;4 .)
b) What are the potentials Va;b at nodes a and b relative to ground?

回答 (1)

用戶10012

2013-02-28 4:18 pm

✔ 最佳答案

Let current in the left loop = x
current in the center loop = y
current in the right loop = z
They are assumed to flow in the clockwise direction.
For the left loop
10 = xR1 + (x - y)R3
10 = x + 3(x - y)
10 = 4x - 3y ..............(1)
For the center loop
6 = 3(x - y) + 4(z - y) (assume a is the positive side of the 6V)
6 = 3x - 3y + 4z - 4y
6 = 3x - 7y + 4z ............(2)
For the right loop
15 = 4(y - z) - 3z
15 = 4y - 7z ...........(3)
Solving the 3 equations, we get x = 8/23, y = - 66/23 and z = - 87/23.
Current through R1 = x = 8/23 (left to right)
R2 = - z = 87/23 ( right to left)
R3 = x - y = 8/23 + 66/23 = 74/23 ( downwards)
R4 = y - z = - 66/23 + 87/23 = 21/23 ( downwards)
Va = (x - y)R3 = (74/23)(3) = 222/23 = 9.65V
Vb = (y - z)R4 = (21/23)(4) = 84/23 = 3.65V (or 9.65V - 6V = 3.65V)

2013-02-28 08:24:10 補充：
Correction : Current through R2 should be z, not - z, that is - 87/23. Since z is assumed to be clockwise, so current through R2 is anti - clockwise ( from right to left).

2013-02-28 08:29:51 補充：
Note : All currents in mA, since resistances are in Kohms.

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