After publishing the article “Is the Textbook Wrong? – Rethinking the Capacitor Charging and Discharging Experiment,” I received praise and feedback from Teacher Lin Shufen, which made me very happy.
The article is written for communication purposes. As a self-media public account mainly focused on educational essays, it does not aim to impart knowledge but rather to promote communication and personal growth. Therefore, I welcome all constructive criticism, but I do not welcome derogatory remarks that demean my character. Criticisms such as “the author is ignorant in quantum mechanics” are acceptable, and if they can provide easy-to-understand learning materials, I will continue to learn; however, public criticisms like “although the author is a high school physics teacher, they do not have a good grasp of high school physics knowledge” are also acceptable, but please forgive me for not responding. For example, I greatly welcome constructive feedback like the one below. Although such criticism may make me feel a bit “embarrassed” (as I indeed did not read carefully), I can quickly turn that embarrassment into motivation for further learning. After reading such constructive criticism, I can generally optimize and improve my teaching design, maintaining my teaching style while not becoming complacent. After reading the criticism below, I wrote an article titled “Using Deep Teaching to Maintain the ‘Authority’ of Textbooks,” which further promoted my learning. Today, I will share this learning process.
Yesterday’s article speculated that digital voltmeters and voltage sensors can be considered ideal voltmeters based on high school physics knowledge. Is this really the case? Let’s ask Mr. DS:
Author: The working principle of a digital voltmeter.
DS: A digital voltmeter (Digital Voltmeter, DVM) is an electronic instrument that measures voltage using digital technology, with its core function being to convert analog voltage signals into digital signals and display the results. Below is a detailed step-by-step explanation of its working principle:
1. Input Circuit Processing
Function: Receives the voltage signal to be measured and performs preliminary processing.
Attenuation/Voltage Division: If the input voltage exceeds the range, it is reduced to a manageable level through a voltage divider network (such as high-precision resistors).
Protection Circuit: Uses diodes, fuses, etc., to prevent overvoltage or reverse voltage from damaging internal components.
High Input Impedance: Typically designed to be megohm level (e.g., 10 MΩ) to minimize the impact on the circuit being measured.
2. Signal Conditioning
Function: Optimizes the signal to meet the input requirements of the Analog-to-Digital Converter (ADC).
Filtering: Uses a low-pass filter to eliminate high-frequency noise (such as electromagnetic interference).
Amplification/Attenuation: Uses operational amplifiers (such as instrumentation amplifiers) to adjust the signal amplitude to match the ADC’s range (e.g., 0-5V).
DC/AC Conversion (optional): If measuring AC voltage, it must be converted to an equivalent DC voltage through rectification and filtering circuits.
3. Analog-to-Digital Conversion (ADC)
Function: Converts the analog voltage into a digital value, which is the core module of the DVM.
Sampling: Samples the analog signal at a fixed frequency (according to the Nyquist theorem, the sampling frequency must be greater than twice the highest frequency of the signal).
Quantization: Discretizes the continuous analog values into a finite number of digital levels (for example, a 12-bit ADC divides the voltage into 2^12=4096 levels).
Conversion Types:
Dual-Slope ADC: Compares the integration time with a reference voltage, has strong anti-interference capability, and high accuracy (commonly used in low-speed, high-precision scenarios).
Successive Approximation (SAR) ADC: Approaches the input voltage using a binary search method, is fast, and suitable for multi-channel measurements.
Reference Voltage (Vref): The accuracy of the ADC directly depends on the stability of the reference voltage, which is usually provided by a high-precision reference source (such as LM4040).
4. Data Processing and Calculation
Function: Converts the raw digital values output by the ADC into actual voltage values.
Calibration Correction: Compensates for non-linear errors or temperature drift through software algorithms.
Range Switching (automatic/manual): Automatically selects the best range based on the input voltage (e.g., 200mV, 2V, 20V range).
Unit Conversion: If displaying AC RMS, peak, or decibel values, mathematical operations are required.
5. Display and Output
Function: Intuitively displays the measurement results.
Display Type: Commonly used LCD or LED digital tubes, supporting multi-digit displays (e.g., 4½ digit display ±19999).
Refresh Rate: Typically updates 2-10 times per second, with high-speed DVMs capable of over a thousand times.
Additional Functions: Data hold, maximum/minimum recording, communication interfaces (such as RS-232, USB), etc.
Key Performance Parameters
1. Resolution: The smallest discernible voltage change (e.g., 1mV).
2. Accuracy: Typically ±(0.1% reading + 1 digit) or higher.
3. Input Impedance: megohm level (reducing loading effects).
4. Range: Microvolts (μV) to kilovolts (kV), extended through voltage divider networks.
Example Process:
Assuming measuring a 12V DC voltage:
1. The input circuit divides 12V to 3V (assuming the range is 20V).
2. The signal conditioning circuit filters out noise and stabilizes the signal.
3. The ADC (e.g., 12-bit, reference voltage 5V) converts 3V to a digital value: \( \frac{3}{5} \times 4095 \approx 2457 \).
4. The microprocessor calculates the actual voltage: \( 2457 \times \frac{20V}{4095} \approx 12.00V \).
5. The result is displayed on the LCD as “12.00 V”.
Advantages Comparison (Digital vs. Analog)
High Accuracy: Avoids human reading errors.
Anti-Interference: Digital filtering suppresses noise.
Multi-Function: Automatic range, data storage, etc.
Easy Integration: Can be expanded into a multimeter (measuring current, resistance, etc.).
Through the above process, the digital voltmeter achieves high precision and reliability in voltage measurement, widely used in electronic R&D, industrial testing, and other fields.
The above learning may be superficial, but it has expanded my knowledge; most importantly, we understand that the digital voltmeter has undergone technical processing in its display, and can essentially be regarded as an “ordinary” but ideal voltmeter with infinite internal resistance.
Author: Let’s also discuss the working principle of voltage sensors.
DS: A voltage sensor is a device that converts voltage signals into measurable, transmittable, or controllable electrical signals, with its core function being **to safely and accurately sense voltage and output standardized signals** (such as analog current, voltage, or digital signals). Below is a detailed explanation of its working principle:
1. Basic Principles and Classification
Voltage sensors can be classified into the following main types based on their working principles:
Resistive Voltage Divider: Measures voltage directly through resistive voltage division (low cost, but no isolation).
Isolated Type (e.g., Hall Effect, Magnetic Coupling): Achieves electrical isolation through electromagnetic induction or magnetic field changes (suitable for high voltage or strong interference environments).
Optical Isolation Type: Uses optocouplers to transmit signals, achieving complete isolation between input and output.
Integrated Module Type: Contains signal conditioning and ADC, directly outputting digital signals (e.g., I²C interface).
2. Step-by-Step Explanation of Working Principles
(1) Resistive Voltage Divider Type Voltage Sensor
Principle: Uses the resistive voltage divider formula \( V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2} \) to reduce the input voltage.
Structure:
High-precision voltage divider resistors: \( R_1 \) (high voltage side) and \( R_2 \) (low voltage side) form a voltage divider network.
Protection Circuit: Parallel TVS diodes prevent overvoltage, and series fuses prevent short circuits.
Output: Directly outputs the divided voltage signal (e.g., 0-5V), which needs to be connected to an ADC or microcontroller.
Applicable Scenarios: Low voltage DC measurement (e.g., Arduino expansion module measuring 0-25V).
(2) Hall Effect Voltage Sensor (Isolated Type)
Principle:
1. The measured voltage is converted into current \( I_{in} = \frac{V_{in}}{R_{in}} \) through the primary side resistor \( R_{in} \).
2. The current flows through the Hall element, generating a magnetic field perpendicular to the direction of the current.
3. The Hall element outputs a voltage \( V_{Hall} \) (Hall voltage) proportional to the magnetic field strength.
4. The operational amplifier amplifies \( V_{Hall} \) to output a standardized signal (e.g., 0-5V or 4-20mA).
Key Features:
Electrical Isolation: No direct electrical connection between the primary side (measured circuit) and the secondary side (output circuit).
Wide Range: Can measure DC/AC voltages (e.g., 0-1000V).
Applications: Electric vehicle battery management systems (BMS), industrial inverter voltage monitoring.
(3) Optical Isolation Type Voltage Sensor
Principle:
1. The input voltage is converted into a low voltage signal through a voltage divider circuit.
2. The low voltage signal drives an LED to emit light, which is received by a phototransistor.
3. The output current of the photodetector is proportional to the input voltage and is conditioned before output.
Advantages: Complete isolation between input and output, strong electromagnetic interference resistance.
Typical Applications: Voltage monitoring in medical devices, industrial PLCs.
(4) Integrated Digital Voltage Sensor (e.g., INA219)
Principle:
1. Contains precision voltage divider resistors and a 16-bit ADC.
2. Directly outputs digital voltage values via I²C interface.
3. Integrates calculation functions to measure voltage, current, and power simultaneously.
Features: No external circuit required, suitable for embedded systems (e.g., Raspberry Pi, ESP32).
3. Key Parameters and Selection
1. Measurement Range:
DC: 0-5V, 0-1000V; AC: 0-220V (RMS).
2. Accuracy:
Generally ±1% to ±0.1% (high-precision types can reach ±0.05%).
3. Isolation Voltage:
– Isolated sensors must specify isolation withstand voltage (e.g., 2500Vrms/1 minute).
4. Response Time:
– Hall effect types are usually in microseconds, while optical isolation types may reach milliseconds.
5. Output Forms:
– Analog: 0-5V, 4-20mA; Digital: I²C, SPI, UART.
4. Typical Application Scenarios
– Electric Vehicles: Battery pack voltage monitoring (requires isolation and high precision).
– Solar Inverters: DC bus voltage detection (resistant to high voltage and surges).
– Smart Meters: AC grid voltage sampling (compliant with safety isolation requirements).
– Industrial PLCs: Monitoring device power supply voltage (resistant to electromagnetic interference).
5. Example: Hall Effect Sensor Measuring 380V AC Voltage
1. Input Processing: 380V AC is converted to 10mA current through the primary side resistor \( R_{in} = 38kΩ \).
2. Hall Effect Conversion: The current flows through the Hall element, outputting a voltage proportional to the current.
3. Signal Conditioning: The operational amplifier amplifies the Hall voltage to a 0-5V DC signal.
4. Isolated Output: The secondary circuit is isolated through an optocoupler, outputting to the PLC’s analog input module.
5. Result Display: The PLC converts the signal to the actual voltage value (e.g., 380V ±1%).
6. Voltage Sensor vs. Digital Voltmeter
| Feature | Voltage Sensor | Digital Voltmeter (DVM) ||——-|—————-|——————-||Core Function| Converts voltage to standardized signal | Directly measures and displays voltage value ||Output Form| Analog/Digital signal (requires external device) | Direct digital display ||Isolation Capability| Most support isolation | Usually no isolation (unless specially designed) ||Integration Level | Can be integrated into systems (e.g., PCB) | Standalone instrument ||Typical Applications| Automation control embedded systems | Laboratory measurement, field maintenance |
7. Design Considerations
Safety: High voltage measurements must use isolated sensors and comply with safety standards (e.g., IEC 61010).
Anti-Interference: In strong electromagnetic environments, prioritize magnetic or optical isolation solutions.
Temperature Drift Compensation: High-precision sensors need built-in temperature sensors and compensation algorithms.
Power Consumption: In battery-powered scenarios, choose low-power models (e.g., integrated sleep mode).
Voltage sensors achieve a wide range of voltage monitoring needs from low-voltage electronic circuits to high-voltage power systems through flexible signal conversion and isolation technologies, serving as the “perceptive nerve” of modern automation and energy systems.
Based on high school physics knowledge, it is difficult to fully understand the above content. It is noted that there are many types of voltage sensors, and by comparing “voltage sensors” and “digital voltmeters,” it can be inferred that voltage sensors can also be regarded as ideal voltmeters. Therefore, let’s ask again.
Author: From the perspective of high school physics, can voltage sensors be understood as ideal voltmeters?
From the perspective of high school physics, voltage sensors and ideal voltmeters have both similarities and essential differences. We can gradually understand this through the following analysis:
1. Characteristics of Ideal Voltmeters (High School Model)
In high school physics, ideal voltmeters are simplified to the following features:
Infinite internal resistance: When measuring, it does not draw current from the measured circuit, so its impact on the original circuit can be ignored.
Directly displays voltage value: No external circuit is needed; it can be directly connected across the measured circuit to read the value.
No energy loss: Theoretically, it does not consume electrical energy (because no current flows).
2. Core Function of Voltage Sensors
The core of voltage sensors is to convert voltage signals into another usable form (such as analog signals, digital signals, or isolated signals), characterized by:
Possible introduction of internal resistance: For example, the resistive voltage divider in the voltage sensor will form a finite internal resistance, which may affect the measured circuit.
Requires external circuits: The output signal usually needs amplification, filtering, or digital processing.
May isolate or convert signals: For example, through the Hall effect or optocouplers to achieve electrical isolation.
3. Similarity: Resistive Voltage Divider Sensor ≈ Non-Ideal Voltmeter
Taking the simplest resistive voltage divider type voltage sensor as an example (e.g., Arduino voltage detection module):
Principle: Reduces the input voltage through the voltage divider formula \( V_{out} = V_{in} \cdot \frac{R_2}{R_1 + R_2} \).
Equivalent internal resistance: The total resistance of the voltage divider network \( R_1 + R_2 \) will be in parallel with the measured circuit (similar to the internal resistance of a voltmeter).
Impact on the circuit: If the impedance of the measured circuit is comparable to the voltage divider resistors, it will lead to measurement errors (similar to a real voltmeter).
At this point, the resistive voltage divider sensor can be approximated as a “non-ideal voltmeter” (with finite internal resistance, which may affect the circuit).
4. Essential Differences: Function and Design Goals
| Feature | Ideal Voltmeter (High School Model) | Voltage Sensor ||——–|———————|———–|| Core Goal | Directly measure and display voltage | Convert voltage to standardized signal for use by other systems || Internal Resistance | Infinite (theoretical model) | Finite (e.g., resistive type) or achieved through isolation || Output Form | Directly displays value (e.g., “5.0 V”) | Analog signal (0-5V), digital signal (I²C), etc. || Isolation Capability | No isolation | Can isolate high voltage (e.g., Hall sensor) || Application Scenarios | Laboratory measurement, simple circuit analysis | Embedded systems, industrial control, automation |
5. Key Differences Illustrated
Scenario 1: Measuring the voltage of a high internal resistance power supply
Ideal Voltmeter: Infinite internal resistance, accurately measures voltage (\( V = \varepsilon \), electromotive force of the power supply).
Resistive Voltage Sensor: If the voltage divider resistors \( R_1 + R_2 = 100kΩ \), and the power supply internal resistance is \( 1MΩ \), the sensor’s internal resistance will significantly shunt, leading to a lower measurement value.
Scenario 2: Measuring high AC voltage (e.g., 220V mains)
Ideal Voltmeter: Cannot measure directly (requires voltage reduction and no isolation, dangerous!).
Hall Voltage Sensor: Safely converts high voltage to low voltage signals through electromagnetic isolation, and can be integrated into control systems.
6. Simplified Understanding from a High School Perspective
If we only consider the resistive voltage divider sensor, it can be analogized as a kind of “actual voltmeter” (with finite internal resistance), but it should be noted:
1. Sensors usually require external circuits (such as ADCs, microcontrollers) to display or process signals.
2. Ideal voltmeters are theoretical tools, while sensors are engineering devices that must consider practical issues such as safety and anti-interference during design.
7. Conclusion: When Can They Be Considered Equivalent?
Low voltage, low impedance circuits: If the sensor’s internal resistance is much greater than the impedance of the measured circuit (e.g., measuring battery voltage), the resistive voltage divider sensor can be approximated as an ideal voltmeter.
High voltage, high precision, or isolation scenarios: Sensors (such as Hall effect types) must be used, and the differences from ideal voltmeters are significant.
In summary:
In simple scenarios (such as low voltage, low impedance circuits), resistive voltage sensors can be approximated as “non-ideal voltmeters”; however, from the perspective of function and design goals, voltage sensors are more complex and cannot be completely equated with ideal voltmeters.
Unfortunately, the author’s inference was incorrect; not all voltage sensors can be regarded as ideal voltmeters. Therefore, when using the DIS system for capacitor charging and discharging experiments, it is essential to choose the right sensor.
Based on the recent three days of teaching discussions on “Capacitance of Capacitors,” I believe the following two points are very important:
Point One: Experiments in the classroom need to be real and clear, which requires that the experimental equipment and its parameters must be introduced clearly; otherwise, it will lead students to remember confusing experimental conclusions. It is noted that many provinces base experimental questions on real experiments, so the experimental results may differ from the textbook or the confusing experimental conclusions in actual classrooms. Therefore, from both an examination perspective and a competency teaching perspective, conducting experiments in a confusing manner in the classroom is a very undesirable teaching method.
Point Two: Learning high school physics knowledge through inquiry-based learning should not use information technology aids like the DIS system. However, we do need to start early, allowing students to quickly master information technology. Therefore, in practical activities aimed at consolidating high school physics knowledge, such as measurement experiments, it is advisable to encourage students to boldly and actively use sensors and other information technology means—cross-disciplinary practical courses are probably based on this concept!