The prerequisite for the calculation of circuit problems is to correctly identify the circuit and make clear the connection between the various parts. For more complex circuits, the original circuit should be simplified to the equivalent circuit for analysis and calculation.

There are many ways to identify circuits, and INFINITECH introduces ten methods with specific examples.

1. Feature recognition method

The characteristics of the series parallel circuit are: the current in the series circuit does not fork, the potential of each point is gradually reduced, the current in the parallel circuit forks, the two ends of each branch are equal potential, and the voltage between the two ends is equal. Identifying a circuit according to the characteristics of a series-parallel circuit is one of the most basic ways to simplify a circuit.

Example: Try to draw the equivalent circuit shown in Figure 1.

Solution: Let the current flow in from the A end, bifurcate at the a point, converge at the b point, and flow out from the B end. The potential of each point of branches A-R1-B and A-R2-R3 (R4) -B decreases gradually, and the voltage between two points a and b of the two branches is equal. Therefore, R3 and R4 are connected in series with R2 after being connected in parallel, and then in parallel with R1, and the equivalent circuit is shown in Figure 2.

2. Telescopic flipping method

When connecting the circuit in the laboratory, it is often possible to operate in this way, and the unimpeded wire can be extended or shortened, or it can be turned over and turned over, or the two ends of the branch can be kept stationary when it is turned over. A wire can also slide along other wires from the node where it is located, but it cannot pass over the component. This provides a way to simplify the circuit, and we call this method the telescopic flipping method.

Example: Draw the equivalent circuit in Figure 3.

Solution: First shorten the wires connecting nodes a and c, and extend the wires connecting nodes b and d to the outside of the R3-C-R4 branch, as shown in Figure 4.

Then shrink the wires connecting nodes a and c to a point, shrink the wires connecting nodes b and d to a point, and connect R5 to the extension wire of node d (Figure 5). It can be seen that R2, R3 and R4 are connected in parallel, and then R1 and R5 are connected in series to the power supply.

3. Current direction method

Current is the core of the analysis circuit. Starting from the positive electrode of the power supply (passive circuit can assume that the current flows from one end to the other end) along the direction of the current, through the resistance around the external circuit for a week to the negative electrode of the power supply, all the current flows through the resistor without fork in turn are series, and all the current flows through the resistor with fork respectively are in parallel.

Example: Try to draw the equivalent circuit shown in Figure 6.

Solution: The current flows out of the positive terminal of the power supply through point A and is divided into three ways (AB wire can be reduced to a point), travels through the external circuit for a week, and flows into the negative terminal of the power supply from point D. The first route goes through R1 to point D, the second route goes through R2 to point C, and the third route goes through R3 to point C. Obviously, R2 and R3 are connected in parallel between two AC points. The second and third currents converge at point c and reach point D through R4. It can be seen that R2 and R3 are connected in series with R4 and then connected with R1 in parallel, as shown in Figure 7.

4. Equipotential method

In more complex circuits, it is often possible to find points of equal potential, and all points of equal potential are reduced to a single point, or drawn on a line segment. When there is a non-power supply element between the two equal potential points, it can be removed without consideration; When a branch has neither power supply nor current, you can cancel this branch. We call this method of simplified circuits the equal potential method.

For example, as shown in Figure 8, given that R1 = R2 = R3 = R4 = 2Ω, find the total resistance between two points A and B.

Solution: Imagine that two points A and B are respectively connected to the positive and negative poles of the power supply for analysis, and the potential of two points A and D is equal, and the potential of two points B and C is also equal, respectively drawn into two line segments. Resistor R1 is connected at two points A and C, that is, at two points A and B; R2 is connected to two points C and D, that is, to two points B and A; R3 is connected at two points D and B, that is, at two points A and B, and R4 is also connected at two points A and B. It can be seen that the four resistors are connected in parallel between two points A and B (Figure 9). So PAB is equal to 3Ω.

5. Branch node method

A node is the junction of several branches in a circuit. The so-called branch node method is to number each node (convention: the power supply is the first node, from the positive terminal to the negative terminal of the power supply, the nodes passed by in order of 1, 2, 3......) The branch from node 1 is drawn towards the negative terminal of the power supply. There may be multiple branches (provision: different branches can not repeat through the same resistance) to reach the negative terminal of the power supply, the principle of drawing is to draw the branch with fewer nodes first, and then draw the branch with more nodes. Then, following this principle, draw the branch from node 2. The remainder of the analogy, and finally the remaining resistance according to the position of its two ends.

Example: Draw the equivalent circuit shown in Figure 10.

Solution: There are five nodes in Figure 10:1, 2, 3, 4, and 5. According to the principle of branch node method, there are two branches with fewer nodes coming out of the positive terminal of the power supply (node 1) : R1, R2, and R5 branches and R1, R5, and R4 branches. Take one of the R1, R2 and R5 branches and draw as shown in Figure 11.

Starting from the second node, there are two branches to reach the negative terminal, one is R5, R4, the number of nodes is 3, and the other is R5, R3, R5, the number of nodes is 4, and it is not advisable to repeat R6. Therefore, R5 and R4 branches should be drawn again, and finally the remaining resistance R3 should be drawn, as shown in Figure 12.

6. Geometric deformation method

The geometric deformation method is to carry out geometric deformation of a given circuit according to the characteristics that the wires in the circuit can be arbitrarily extended, shortened, rotated or translated, so as to further determine the connection relationship of circuit components and draw an equivalent circuit diagram.

Example: Draw the equivalent circuit in Figure 13.

Solution: The ac branch wire is shortened, the circuit is geometrically deformed, and Figure 14 can be obtained. Then, ac is shrunk to a point, and bd is also shrunk to a point. It is obvious that R1, R2 and R5 are in parallel, and then in series with R4 (Figure 15).

7. Remove the resistance method

According to the characteristics of the series parallel circuit, in the series circuit, remove any resistance, other resistors no current through, then these resistors are connected in series; In a parallel circuit, remove any resistance, other resistors still have current through, then these resistors are connected in parallel.

For example: Take Figure 13 as an example again, let the current flow in from end A and out from end B, and remove R2 first. It can be seen from Figure 16 that there is current passing through R1 and R3. Then remove resistor R1, and it can be seen from Figure 17 that R2 and R3 still have current passing through. Similarly, when the resistor R3 is removed, R1 and R2 also have current through the characteristics of the parallel circuit, R1, R2 and R3 are in parallel, and then in series with R4.

8. Independent branch method

Let the current flow from the positive electrode of the power supply, under the principle of not repeating through the same component, see how many of them flow back to the negative electrode of the power supply, and there are several independent branches. The remaining resistors not contained in the separate branches are filled at the positions of their ends. When using this method, select the independent branch to include the wire.

Example: Draw the equivalent circuit in Figure 18.

• Solution 1: Select A-R2-R3-C-B as one independent branch, A-R1-R5-B as the other independent branch, and the remaining resistance R4 is connected between D and C, as shown in Figure 19.

• Scheme 2: Select A-R1-D-R4-C-B as an independent branch, and then arrange the positions of R2, R3 and R5 respectively to form equivalent circuit Figure 20.

• Scheme 3: Select A-R2-R3-C-R4-D-R5-B as an independent branch, and then connect R1 to AD, and the wire is connected between C and B, as shown in Figure 21, the result still cannot intuitively judge the serial-parallel relationship of the resistance, so it is necessary to include the unimpeded wire when selecting the independent branch.

9. Node crossover method

Number the nodes in the known circuit, in order of potential from high to low with 1, 2, 3... The number is marked (the node connected to the positive electrode of the power supply has the highest potential, the node connected to the negative electrode of the power supply has the lowest potential, and the nodes with the same potential are used in the same number, and are combined into a point). Then the nodes are rearranged according to the level of potential, and then the components are connected between the corresponding two nodes, and the equivalent circuit can be drawn.

Example: Draw the equivalent circuit shown in Figure 22.

Solution: Node numbers are shown in Figure 22. Nodes are arranged, and nodes 1 and 23 are arranged successively on a straight line, as shown in Figure 23. The components are returned, and R1, R2, R3 and R4 are connected respectively to the equivalent circuits arranged in 1 and 2, as shown in Figure 24.

10. Ammeter pickup method

If the complex circuit is connected with an electric meter, regardless of the influence of the internal resistance of the ammeter A and the voltmeter V, because the internal resistance of the ammeter is zero, it can be removed and replaced with an unimpeded wire; Because the voltmeter has great internal resistance, it can be removed as an open circuit. Use the above method to draw the equivalent electricity to understand the connection relationship, and then fill the meter to the corresponding position of the circuit.

For example, in the circuit shown in Figure 25, the influence of the internal resistance of the meter is ignored, and try to draw its equivalent circuit.

Solution: First, the current is removed, a wire is used to replace it, and then the voltmeter is removed as an open circuit. Figure 26 is obtained. Then the ammeter and voltmeter are connected to the corresponding positions in the circuit according to Figure 25, as shown in Figure 27.