How to calculate the equivalent resistance and how to find the equivalent resistance

The equivalent resistance r of the equivalent resistance is total = (5 6) * r

Let the cubes be ABCD-EFGH, and their correspondence is A on E, B on F, C on G, D on H

Since the resistors are equal, find the resistance on the diagonal, and the circuit has symmetry. Let the current i flow from A to G, the current on the three edges from point A is i1=(1 3)*i, the current on the other two edges from B, D, and E is i2=(1 6)*i, the current to F, H, and C is also (1 6)*i, and the current to G is three (1 3)*iLet the voltage between AG be U, and the voltage along the AEHG branch is also U, U=i1*R+I2*R+I1*R=(5 6)*I*R=IR total.

So r total = (5 6) * r

Any resistor in an electrical circuit, no matter how many there are, can be replaced by a resistor. It does not affect the voltage at both ends of the original circuit and the change of current intensity in the circuit.

This equivalent resistance is calculated by the equivalent series-parallel formula of multiple resistors. It can also be said that after replacing the original resistors, this equivalent resistor will not have any effect on the voltage and current flow of the entire circuit, so this resistor is called the equivalent resistance in the loop.

First, the circuit is converted equivalently, and it can be seen that the potentials of c and d are equal. The 4R can be removed. After simplification, the equivalent resistance between abs is obtained. (See diagram for steps).

The role of several connected resistors can be replaced by a resistor, which is the equivalent resistance of those resistors. There are several ways to find the equivalent resistance:

1. The series connection of resistors.

Taking the three resistor connections as an example, the circuit is shown in the figure below.

According to the series characteristics of the resistors, it can be deduced that the equivalent resistance is equal to the sum of the series resistances, that is, r=r1+r2+r3+......rn。

It can be seen that the more series resistance, the greater the equivalent resistance; If the resistance values of each resistor are the same, the equivalent resistance is r=nr1.

Second, the parallel connection of resistors.

The circuit is shown in the figure below.

According to the characteristics of resistor paralleling, it can be deduced that the reciprocal of the equivalent resistance is equal to the sum of the reciprocal of each parallel resistor, that is: 1 r=1 r1+1 r2+1 r3+......1/rn。

This shows that the more parallel resistors, the smaller the equivalent resistance, and the equivalent resistance is smaller than the smallest resistance; If the values of each resistance are the same, then the equivalent resistance r=r1 n; If two resistors are connected in parallel, then the equivalent resistance r=r1r2 r1+r2.

3. Mixing of resistors.

In the actual circuit, it is rare to have a simple resistor in series or parallel, and it is more common to have both series and parallel, that is, a mixed circuit with resistance.

For the calculation of the equivalent resistance of the hybrid circuit, the connection relationship between the resistors is relatively easy to determine.

The solution method is as follows: first partial, then whole, that is, first determine the series and parallel relationship of local resistance, according to the calculation formula of series and parallel equivalent resistance, find the local equivalent resistance respectively, and then gradually simplify the circuit, and finally find the total equivalent resistance.

This is the hybrid circuit, in the hybrid circuit, according to the structure of the circuit to be calculated in parallel, series connection.

For example: r1=10, r2=10, r3=15, find the equivalent resistance of the circuit. Take a look at the two pictures below.

The figure on the left shows the circuit structure of R1 and R3 in series and then in parallel with R2, so the calculation process is:

First, calculate the equivalent resistance of R1 and R3 in series: R13 = R1 + R3 = 10 + 15 = 25

Then calculate the total equivalent resistance of the circuit: r and = r13*r2 (r13+r2)=25*10 (25+10)=

The figure on the right shows the circuit structure of R1 and R3 in parallel and then in series with R2, so the calculation process is:

rand = r1r3 (r1+r3)=10*15 (10+15)=6

r string = r sum + r 2 = 6 + 10 = 16

The attached drawings are as follows:

<> solution: decouple the coupling circuit, xl1=2 6=12( )xl2=2 2=4( )xm=2 3=6( )xc=1 (2

According to KVL:

U (phasor) = J12 I1 (phasor) + J6 I2 (phasor) - J5 I1 (phasor) = J7 I1 (phasor) + J6 I2 (phasor);

U(phasor) = (1+J4) i2 (phasor) + J6 i1 (phasor).

Get: i1 (phasor) = (2-j1) i2 (phasor).

According to KCL: i (phasor) = i1 (phasor) + i2 (phasor) = (2-j1) i2 (phasor) + i2 (phasor) = (1-j1) i2 (phasor).

So: i2 (phasor) = (phasor).

i1 (phasor) = (2-j1) (phasor) = (phasor).

Therefore: U (phasor) = J7 (phasor) + J6 (phasor) = (phasor).

So: z=u(phasor) i(phasor)=

The second simplification method:

l1-m=6-3=3（h），xl1=ω×l1-m）=2×（6-3）=6（ω）

xl2=ω×l2-m）=2×（2-3）=-2（ω）

xl3=ω×m=2×3=6（ω）xc=1/（ωc）=1/（2×

This results in the equivalent circuit in the diagram above, so:

z=j6+（j6-j5）∥（1-j2）=j6+j1×（1-j2）/（j1+1-j2）=j6+（2+j1）/（1-j1）=j6+（2+j1）×（1+j1）/2=j6+（

Your decoupling T-equivalent circuit is drawing the wrong one;

Equivalent resistance refers to the total resistance produced by multiple resistive elements in a circuit under certain conditions, which can be calculated as follows:

Calculation method of the equivalent resistance of the series resistance: The equivalent resistance of the series resistance is the sum of the resistors. That is, the electrical delay or drag reduction values of all series resistors in the circuit are added to obtain their equivalent resistances.

Calculation method of the equivalent resistance of the parallel resistor: The equivalent resistance of the parallel resistor is the sum of the reciprocal of each resistor and then the reciprocal. That is, the resistance values of all parallel resistors in the circuit are added to the reciprocal, and then the sum is taken to the reciprocal to obtain its equivalent resistance.

Calculation method of equivalent resistance of complex circuits: For complex circuits, it can be known that the equivalent resistance of the rubber is calculated by simplifying the circuit step by step. For example, some resistive elements connected in series or parallel can be reduced to a single equivalent resistor, and then the simplified circuit can be simplified until the equivalent resistance of the entire circuit is obtained.

It is important to note that the above methods are based on the assumption that there are only resistive elements in the circuit. In the actual circuit, there may be other components, such as capacitors, inductors, etc., and it is necessary to calculate the equivalent resistance by comprehensively applying the knowledge of circuit analysis.

The picture above shows a balanced bridge, the 30 resistors in the middle have no current, and their equivalent resistance can be calculated by parallel connection of two 30 and 40 resistors and the resistors connected in series with the hand, but the value is 35.

If the bridge is unbalanced, it can be calculated by y-equivalent transformation into a simple potato-pure resistance network.

Because this circuit is a symmetrical circuit, the voltage of the electric masses at both ends of the 30 ohm resistor in the middle is equal, and no current flows, which is equivalent to a short circuit or an open circuit, so that its equivalent resistance is equal to (30 2) + (40 sen or reed 2) = (30 + 40) 2 with 35 ohms.

The equivalent resistance is found as follows:

The method of finding the equivalent resistance is for the circuit (a): the two 8 resistors of the above blue silver are connected in parallel, which can be equivalent to a 4 resistor; 3 and 6 resistors are connected in parallel, which can be equivalent to a 2 resistor; The lower 8 resistors are connected in parallel with the wires and are shorted. Through analysis, the original circuit can be reduced to:

The equivalent resistance between A and B is REQ 6.

For circuit (b): two 4 resistors in parallel, which can be equivalent to one 2 resistors; Two 10 resistors are connected in parallel, which can be equivalent to a 5 resistor; 7. The resistor is connected between A and B. Through analysis, the original circuit can be reduced to:

The equivalent resistance between A and B is req.

Solving for the equivalent resistance of the Thevenin equivalent circuit and the Norton equivalent circuit can be obtained in several ways.

The equivalent resistance is the input resistance of the passive one-port network obtained after all the independent power supplies in the one-port network are set to zero (the voltage source is short-circuited and the current source is open). It is commonly calculated in the following way:

When there is no controlled source in the network, the equivalent resistance can be calculated by using the method of resistor series-parallel connection and 4-y interchange.

External power supply method (voltage to find current or current to voltage);

Open-circuit voltage, short-circuit current method.

The latter two methods have universal applicability.

A resistor in a circuit that can replace several resistors so that the other parts do not change in any way. Also known as total resistance.

In a series circuit, applying Ohm's law to each resistor yields u1=ir1, u2=ir2, ,..., un=irn, according to the voltage definition, u=u1+u2+....+un, so u=i(r1+r2+...+rn)。

If a resistive element with a resistance value of r is used to replace the original n series resistors, this r satisfies r=r1+r2+....+rn, the current of this resistor element will be the same as that of the original series circuit.

r is called the equivalent resistance of a series bump circuit. The equivalent resistance of a series circuit is equal to the sum of the resistors of each component.