Anonymous
Anonymous asked in 科學及數學其他 - 科學 · 8 years ago

# DC circuit

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

|....................................|.................................|.......................................... |

|....................................|..................................|......................................... |

|____________________|__________________|________________________|___................................................|

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................................. ////////

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?

Rating
• wy
Lv 7
8 years ago

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.