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Equivalent change of resistance circuit (Ⅱ)

2022-07-25 15:58:00 【Chenze】

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【2.1】 Equivalent resistance — Y Equivalent transformation

( One ) R1 R2 R3 Calculation formula

( Two ) Y shape and An example of equivalent transformation of

1:Y (Y The resistance of the V-shaped connection depicts a triangle )

2: Y ( The resistance of the triangle connection is depicted Y shape )

3: Parallel conductance is described by

4: Series connection is described by conductance

【2.2】 Voltage source 、 Series and parallel connection of current source

( One ) Series and parallel connection of ideal voltage source

( Two ) Series connection of voltage source and resistance branch 、 Parallel equivalent

( 3、 ... and ) Ideal current source series parallel

( Four ) Series connection of current source and resistance branch 、 Parallel equivalent

【2.1】 Equivalent resistance — Y Equivalent transformation

( triangle ) Of ③ Each vertex is connected by other components , It cannot be simplified directly by series or parallel connection .

therefore , We need to take Connection conversion to Y Shape connection is OK .

First , Suppose you label the three vertices of 1 2 3
The vertices 1 and 2 The resistance of the is marked R12
The vertices 1 and 3 The resistance of the is marked R13
The vertices 2 and 3 The resistance of the is marked R14
Split line
Convert into Y The vertex is constant when the shape is .
And the summit 1 The connected resistance is marked as R1
And the summit 2 The connected resistance is marked as R2
And the summit 3 The connected resistance is marked as R3

( One ) R1 R2 R3 Calculation formula

R1 = R12 x R13 / R12 + R23 + R13
R2 = R23 x R12 / R12 + R23 + R13
R3 = R23 x R13 / R12 + R23 + R13
Above ③ Both denominators are the same , The rest is ③ The sum of the two resistances .
then , This R1, Its molecule is compared with that in the figure above Y Shape connection , It is associated with the vertex 1 The product of two connected resistors . Corresponding ,R2 It is associated with the vertex 2 The product of two connected resistors .R3, It is associated with the vertex 3 The product of two connected resistors .
That's all — Y Equivalent transformation of shape .

( Two ) Y shape and An example of equivalent transformation of

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R1 = 3X5/3+5+2 = 15/9 = 1.5Ω
R2 = 5x2/3+5+2 = 10/10 = 1Ω
R3 = 2x3/3+5+2 = 6/10 = 0.6Ω
benefits ： The problems that cannot be solved by mixed connection can now be solved .
0.6Ω and 1Ω In series 、1 Ohmic and 1Ω In series . Finally, parallel connection is carried out .

So the circuit becomes very simple , The circuit above 1.5Ω unchanged . The following is the sum of the two resistors in series .

Series partial pressure law ：
V04 = 0.89 / 0.89+1.55 x 10 = 3.72V
I = U/R = 3.72/1.6 = 2.33A

There seems to be this universal duality conclusion and law in the circuit
Ⅰ: Series and parallel are dual .
Ⅱ: Capacitive and inductive elements are also dual .
Ⅲ: Voltage and current are also dual .

1:Y (Y The resistance of the V-shaped connection depicts a triangle )

R12 = R1R2 + R2R3 + R3R1 / R3
R23 = R1R2 + R2R3 + R3R1 / R1
R31 = R1R2 + R2R3 + R3R1 / R2

2: Y ( The resistance of the triangle connection is depicted Y shape )

R1 = R12 x R31 / R12+R23+R31
R2 = R23 x R12 / R12+R23+R31
R3 = R31 x R23 / R12+R23+R31

3: Parallel conductance is described by

G1 = G12G23 + G23G31 + G31G12 / G23
G2 = G12G23 + G23G31 + G31G12 / G31
G3 = G12G23 + G23G31 + G31G12 / G12

4: Series connection is described by conductance

G12 = G1G2 / G1 + G2 + G3
G23 = G2G3 / G1 + G2 + G3
G31 = G3G1 / G1 + G2 + G3

【2.2】 Voltage source 、 Series and parallel connection of current source

( One ) Series and parallel connection of ideal voltage source

For the series circuit of voltage ：U = us1 + us2
according to KVL( Kirchhoff's law of voltage ) You know , The potential difference between two points is independent of the path . First specify a path , The virtual path and the actual path in the above figure are ： Left ＋ Right － Of
Then it can be directly equivalent to ① A voltage source
If it is not associated with the virtual direction of the path , Then the potential difference corresponding to the previous one is a negative sign .

For voltage parallel circuits ：U = us1 = us2
Be careful ： The same voltage source can be connected in parallel , The current in the power supply is uncertain .
For the structure of two voltage sources in parallel , In fact, it is equivalent to ① Parallel structure of two voltage sources .
The parallel connection of two voltage sources is equivalent to the following results ：

( Two ) Series connection of voltage source and resistance branch 、 Parallel equivalent

u = us1 + R1i + us2 + R2i = (us1 + us2)+(R1 + R2)i = us + Ri
R1 And R2 The are Left ＋ Right －, The potential difference is ：R1xi & R2xi
The above two figures can be equivalent .

In the above figure is the parallel structure , The voltage source is connected in parallel with any element .
It can be seen from the parallel branches that the voltage is the same .

( 3、 ... and ) Ideal current source series parallel

The ideal current source starts from parallel connection , For parallel circuits with current ：i = is1 + is2 +is3
according to KCL( Kirchhoff's current law ) You know , Incoming current = Outflow current -> A relationship between .
Then it just needs to be equivalent to a current source , There is an equivalent circuit between the two .

The ideal current source starts from series , For the series circuit of current ：i = is1 = is2
For two terminals , It's equivalent to a current flowing in from the left end . From the series connection, we can see that the current is equal everywhere . Equivalent to a current source structure , But it's still with is1 as well as is2 They are equal. .
Be careful ： The same ideal current element can be connected in series , The voltage at each end of the current source is unstable .

( Four ) Series connection of current source and resistance branch 、 Parallel equivalent

i = is1 - u/R1 + is2 - u/R2 = is1 + is2 -(1/R1 + 1/R2)u = is - u/R ( Relational )
In the figure on the left, we can figure out ui Relationship , The picture on the right also exits ui This relationship .
On ＋ Next － Of u, Then the of the whole parallel branch u It's all the same .
according to KCL The current flowing in is is1 and is2 What flows out is u/R1 + u/R2 + i, Then we get the above relationship ！
The picture on the right is the same .