Basic principles of circuit simplification
The complex circuits in junior high school physical electricity can be simplified by the following principles:
☀First: ignoring the wire resistance, it is assumed that the R wire is ≈0. The voltage across the wire with current flowing is zero, and the voltage across the switch can be measured when it is open (no other breakpoints in the circuit).
☀Second: When the switch is closed, it is equivalent to a wire; when the switch is open, it is equivalent to an open circuit, which can be removed from the two nodes of the circuit. When the switch is closed and current flows, the voltage across the switch is zero, and the voltage across the switch can be measured when it is open (there are no other breakpoints in the circuit).
☀Third: The internal resistance of the ammeter is very small. When analyzing the connection mode of the circuit, the place with the ammeter can be regarded as a wire.
☀Fourth: The internal resistance of the voltmeter is very large. When analyzing the connection mode of the circuit, the place with the voltmeter can be regarded as an open circuit and removed from the two nodes of the circuit.
☀Fifth: Short circuit of the electrical appliance (resistance): When the electrical appliance (resistance) and the wire (switch, ammeter) are connected in parallel, there is no current passing through the electrical appliance (as shown in the figure below), and the electrical appliance can be removed from the two nodes of the circuit ( remove).
☀Sixth: The segment Pa of the sliding rheostat is short-circuited by the wire (metal rod) and does not work. After removing the segment Pa, the figure a below becomes figure b.
☀Seventh: Analyze the relationship between total current, total voltage and divided current and divided voltage according to the current and voltage laws of series and parallel circuits "series divided voltage, parallel connected current".
☀Eighth: If the ammeter is connected in series with any electrical appliance, measure the current of that electrical appliance, and if the voltmeter is connected in parallel with any electrical appliance, measure the voltage of that electrical appliance. The voltage measured by the voltmeter can be judged by the slip method and the source method.
☀Ninth: In principle, the voltmeter is required to be connected in parallel in the circuit. When measuring the power supply voltage separately, it can be directly connected to both ends of the power supply.
In general, if the voltmeter is connected in series in the circuit, the measured voltage is the voltage across the power supply (see notes for details). If the ammeter is directly connected to both ends of the power supply, it will be burned out, and the power supply will be short-circuited, burning out the power supply.
☀Tenth: If there are no electrical appliances (except switches and ammeters) on the wire (between nodes), then each point on the wire can be regarded as a point, which can be combined, separated, increased or decreased arbitrarily. (This method is also called node method) For example:
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Circuit Simplification Steps
☀Step 1: Remove the disconnected switch according to the requirements of the topic, and turn the closed switch into a wire.
☀Step 2: Turn the ammeter into a wire (it can also be kept as the case may be).
☀Step 3: Remove the voltmeter.
☀Step 4: Merge (or transpose) the nodes on the wire. (This step is used when there are many electrical appliances in the circuit and they are entangled with each other)
☀Step 5: Draw an equivalent circuit diagram to determine whether the electrical appliances are connected in series or in parallel.
☀Step 6: Use principles 7 and 8 in the original circuit to judge which electrical current and voltage the ammeter and voltmeter measure.
☀Step 7: Add the voltmeter and ammeter to the equivalent circuit diagram, and analyze the relationship between each ammeter and the voltage representation. (Principle Seven)
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Selected lectures on classic examples
☀Example 1: In the following circuit diagram, after the switch S is closed, the reading of the voltmeter V1 is 2.5V, and the reading of V2 is 1V. If the reading of A2 is 0.2A, what is the reading of A1? Find the voltage across the two bulbs.
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Analysis: Step 1: Turn the switch into a wire;
Step 2: Turn the ammeter into a wire;
The third step is to remove the voltmeter.
The fourth step (omitted)
Step 5: Determine the electrical connection method
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Obviously, the two light bulbs are connected in series in the circuit.
Step 6: According to principle 4, know that the voltmeter V2 is disconnected, so there is no current flowing through A1, and the reading is zero; according to the slip method, it is known that V1 is connected in parallel with the power supply, and measure the voltage at both ends of the power supply. V2 and L2 are connected in parallel, and the voltage across L2 is measured.
Step 7: The equivalent circuit diagram is as follows:
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According to the equivalent circuit diagram, it can be seen that the required I1=I2=0.2A
U1=2.5V-1V=1.5V U2=1V
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☀Example 2: As shown in the figure, after the switch s is closed, the relationship between the following voltage representations is, and the relationship between the current representations is ___.
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Analysis: the first step: turn the switch into a wire;
Step 2: Turn the ammeter into a wire;
The third step: remove the voltmeter; the fourth step (omitted);
Step 5: Determine the connection mode of each electrical appliance:
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Step 6: Judge the objects measured by the ammeter and voltmeter according to principles 7 and 8 and the slip method or source removal method.
① In the original circuit, if the voltmeter is removed, it can be found that the ammeters A1 and A2 are connected in series with the light bulb, so the current representation numbers are equal;
② Using the slip method, it can be judged that V1 measures the voltage at both ends of L1, V2 measures the voltage at both ends of the power supply, and V3 measures the voltage at both ends of L2.
Step 7: The equivalent circuit diagram is as follows:
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☀Example 3: After the circuit switch is closed, the readings of v1, v2, and v3 are 8V, 9V, and 4V respectively, so what are the voltages at both ends of L1, L2, and L3?
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The required voltage relationship is: U2=U1+U3 I1=I2
Solution: According to "Ten Principles, Seven Steps", the equivalent circuit diagram of the circuit can be obtained as follows:
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From the equivalent diagram, the following equations can be obtained:
UL1+UL2=8V
UL2+UL3=9V
UL3=4V
Solution: UL1=3v UL2=5v UL3=4V
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☀Example 4: As shown in the figure, it is known that the two light bulbs L1 and L2 are connected in series, then the correct judgment among the three ammeters (ammeter or voltmeter) in ①, ② and ③ is ( )
A. ① is an ammeter, ② and ③ are voltmeters;
B. ① and ③ are voltmeters, and ② is an ammeter;
C. ① and ② are ammeters, and ③ is a voltmeter;
D. ①② and ③ are both ammeters
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Analysis: This question can be answered by the method of elimination. Fill in the tables for the answer to A
Among the three positions, according to the "ten principles, seven steps" circuit diagram is simplified to:
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Obviously, it doesn't fit the title.
Fill in the tables of answer B into the figure, the circuit can be simplified as:
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This method of filling fits the meaning of the question.
Fill in the tables of answer C into the circuit, circuit L1 is disconnected, and the simplified circuit diagram is the same as answer A, which does not meet the meaning of the question. Fill in the tables of the answers to D in the figure, the power supply is short-circuited, and no current flows through the two bulbs, which does not meet the meaning of the question. So choose answer B.
