Electronic Basics
Vacuum tubes are electronic devices that control the flow of electric current within a sealed glass envelope. This envelope contains a heated cathode (emitter) and a cold anode (collector).
Here's a simplified breakdown of how a vacuum tube works:
- Heating: The cathode is heated to a high temperature. This causes electrons to be emitted from the cathode, a process known as thermionic emission.
- Electric Field: A positive voltage is applied to the anode, creating an electric field between the cathode and anode.
- Electron Flow: The emitted electrons are attracted to the positive anode, creating a flow of electric current.
- Control Grid: A third element, called the control grid, is placed between the cathode and anode. By applying a voltage to the control grid, we can control the number of electrons that reach the anode, thus regulating the current flow.
Applications of Vacuum Tubes:
- Audio amplification: In early radios and amplifiers, vacuum tubes were used to amplify audio signals.
- Television: In older television sets, vacuum tubes were used in the picture tube to create the image.
- Computers: Early computers relied heavily on vacuum tubes for their logic and memory functions.
While vacuum tubes have been largely replaced by solid-state devices like transistors, they are still used in some specialized applications, such as high-power amplifiers and vintage audio equipment.
The first transistor was invented in 1947 by John Bardeen, Walter Brattain, and William Shockley at Bell Labs. It was a point-contact transistor, a type that used two metal points in contact with a semiconductor material to control the flow of current.
This invention was a major breakthrough in electronics and paved the way for the development of modern computers, smartphones, and countless other electronic devices.
The first semiconductors were discovered in the early 19th century, but it wasn't until the mid-20th century that they were developed into practical devices.
Here are some key milestones in the history of semiconductors:
- 1833: Michael Faraday discovered the photovoltaic effect, which is the conversion of light into electricity in certain materials.
- 1873: Frederick Guthrie observed that a selenium crystal could conduct electricity better in one direction than the other.
- 1904: John Ambrose Fleming invented the vacuum tube, which used a heated filament to emit electrons.
- 1925: Julius Edgar Lilienfeld filed a patent for a field-effect transistor (FET), a type of semiconductor device that controls the flow of current using an electric field.
- 1947: John Bardeen, Walter Brattain, and William Shockley invented the point-contact transistor, a type of semiconductor device that used two metal points in contact with a semiconductor material to control the flow of current.
- 1950s: The first commercial transistors were produced, and the semiconductor industry began to grow rapidly.
Semiconductors have since become essential components in a wide range of electronic devices, including computers, smartphones, televisions, and cars.
Electronics Are Powering Our World
Electronics is the study of devices that use electricity. These devices, like computers and phones, are essential to our daily lives. They work by controlling the flow of tiny particles called electrons.
Electronics have changed the way we communicate, entertain ourselves, and even receive healthcare. For example, smartphones have revolutionized how we connect with others and access information. Medical devices help doctors diagnose and treat illnesses more effectively.
The semiconductor industry is the backbone of electronics. It produces tiny chips that are the building blocks of electronic devices. These chips are getting smaller and more powerful all the time.
However, the rapid growth of electronics also raises concerns. There are privacy issues, as devices collect a lot of personal data. Some people worry about the environmental impact of electronic waste.
In the future, we can expect even more exciting developments in electronics. Artificial intelligence, quantum computing, and nanotechnology are just a few of the emerging technologies that could change our world.
Overall, electronics have had a profound impact on society. As technology continues to advance, it's important to consider both the benefits and challenges they present.
The Evolution of Electronics
From the discovery of the electron to the invention of the integrated circuit, the evolution of electronics has been a remarkable journey. This technological odyssey has shaped our world, transforming the way we communicate, work, and live.
The field was born in the late 19th century with the identification of the electron and the subsequent development of vacuum tubes. These tubes, capable of amplifying and rectifying electrical signals, laid the foundation for radio, television, and long-distance telephony.
While vacuum tubes were instrumental in the early growth of electronics, their limitations became apparent as technology progressed. The invention of the transistor in 1947 marked a turning point, offering a smaller, more reliable, and energy-efficient alternative. Transistors quickly became the cornerstone of electronic devices, powering everything from computers to smartphones.
The development of the MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) in the 1950s further revolutionized electronics. Its compact size and high scalability made it ideal for mass production and integration into various devices.
As electronic circuits grew in complexity, the need for miniaturization became evident. The invention of the integrated circuit, which combined multiple components on a single chip, addressed this challenge and paved the way for the development of microprocessors and modern computers.
Today, electronics continue to shape our world, powering everything from communication devices to medical equipment. The ongoing advancements in semiconductor technology and emerging fields like artificial intelligence and quantum computing promise even more exciting developments in the future.
Understanding the electronic components
electronic components are the essential building blocks of the electronic devices that power our world. These discrete devices, available in individual form or as part of larger packages, manipulate electrons and their associated fields to perform specific functions.
datasheet for an electronic component provides comprehensive technical information, including specifications, characteristics, and performance. This document is invaluable for engineers and technicians designing and building electronic circuits.
Discrete circuits are composed of individual electronic components, each with a unique function. These components, often made from semiconductor materials like transistors, are the fundamental units of electronic systems.
Electronic components have electrical terminals or leads that connect to other components to form electronic circuits. These circuits can perform a wide range of functions, from amplifying signals to generating oscillations. Basic electronic components may be packaged individually, as arrays or networks, or integrated into larger packages like integrated circuits.
The following list focuses on discrete electronic components, treating packaged components as individual entities in their own right.
Categorize common electronic components based on their function and properties:
Passive Components
- Resistors: Control the flow of current in a circuit.
- Capacitors: Store electrical energy.
- Inductors: Oppose changes in current.
- Transformers: Transfer electrical energy between circuits.
Active Components
- Transistors: Amplify or switch electrical signals.
- Diodes: Allow current to flow in one direction only.
- Integrated Circuits (ICs): Contain multiple interconnected components on a single chip.
Optoelectronic Components
- Light-Emitting Diodes (LEDs): Convert electrical energy into light.
- Photodiodes: Convert light into electrical energy.
- Phototransistors: Combine the functions of a photodiode and a transistor.
Electromechanical Components
- Relays: Control a large current with a small signal.
- Motors: Convert electrical energy into mechanical energy.
- Sensors: Detect physical quantities like temperature, pressure, or light.
Other Components
- Batteries: Store electrical energy chemically.
- Fuses: Protect circuits from excessive current.
- Connectors: Join electrical circuits together.
- Switches: Control the flow of current.
Resistor
Resistors are fundamental electronic components that play a crucial role in controlling the flow of electric current within a circuit. They have a specific electrical resistance, measured in ohms (Ω), which determines how much they resist the passage of current.
Key Functions:
- Limiting Current: Resistors are used to limit the amount of current flowing through a circuit, preventing excessive current that could damage components.
- Dividing Voltage: By placing resistors in series, you can divide the voltage across them proportionally. This is useful in circuits that require different voltage levels.
- Setting Time Constants: In circuits involving capacitors or inductors, resistors help determine the time constant, which affects the circuit's response to changes in voltage or current.
- Creating Voltage References: Precision resistors can be used to create voltage references, which are essential for accurate measurements and control of electronic circuits.
Types of Resistors:
- Carbon Film Resistors: The most common type, made by depositing a thin film of carbon onto a ceramic substrate.
- Metal Film Resistors: Offer better precision and stability than carbon film resistors.
- Wirewound Resistors: Constructed from a wire wrapped around a ceramic core, suitable for high-power applications.
- Variable Resistors (Potentiometers): Allow the resistance to be adjusted manually.
- The first significant figure of component value (left side)
- The second significant figure (some precision resistors have a third significant figure, and thus five bands).
- The decimal multiplier (number of trailing zeroes, or power of 10 multiplier)
- If present, indicates tolerance of value in per cent (no band means 20%)
Tight tolerance resistors may have three bands for significant figures rather than two, or an additional band indicating temperature coefficient of resistance (TCR), in units of ppm/K.
All coded components have at least two value bands and a multiplier; other bands are optional.
The standard colour code per IEC 60062:2016 is as follows:
Resistor Values and Tolerance
Resistor values are often standardized to specific numbers known as preferred values. These values are organized into E series based on their tolerance, which indicates the maximum allowable deviation from the specified value.
- E6 series: Used for resistors with a 20% tolerance. The values in this series are approximately 6√10 times the previous value.
- E12 series: Used for resistors with a 10% tolerance. The values in this series are approximately 12√10 times the previous value.
- Higher E series: Used for resistors with tighter tolerances, such as E24 (5%), E48 (2.5%), and E96 (1%).
The separation between values in an E series is carefully chosen to ensure that the extreme values of adjacent resistors just overlap when considering their tolerance range. This prevents overlapping resistance values within the same tolerance range.
Zero-ohm resistors are a special case. They have a resistance of zero ohms and are primarily used as conductive links or jumpers on printed circuit boards. They are often marked with a single black band.
Capacitor
Capacitors: Storing Electrical Energy
Capacitors are essential electronic components that store electrical energy in an electric field. They play a crucial role in various applications, including filtering, timing, and energy storage.
Capacitor Marking:
Capacitors are often marked with coloured bands or dots to indicate their capacitance value. The typical marking scheme involves four or more colours:
- First two colours: Represent the first and second most significant digits of the capacitance value in picofarads (pF).
- Third colour: Represents the decimal multiplier (number of zeros).
- Fourth and subsequent colours: May have different meanings depending on the capacitor type and manufacturer, such as tolerance, voltage rating, or temperature coefficient.
Low-Tolerance Capacitors:
For capacitors with low tolerances (high precision), the first three digits of the capacitance value might be indicated instead of just the first two. This provides more accurate information about the component's value.
Cylindrical Capacitors:
Cylindrical capacitors, often used in high-voltage applications, may have a similar appearance to resistors. However, they can be distinguished by their larger size and the presence of a small hole or indentation on one end.
Inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil.
When the current flowing through the coil changes, the time-varying magnetic field induces an electromotive force (emf) (voltage) in the conductor, described by Faraday's law of induction. According to Lenz's law, the induced voltage has a polarity (direction) which opposes the change in current that created it. As a result, inductors oppose any changes in current through them.
An inductor is characterized by its inductance, which is the ratio of the voltage to the rate of change of current. In the International System of Units (SI), the unit of inductance is the Henry (H) named for 19th century American scientist Joseph Henry. In the measurement of magnetic circuits, it is equivalent to weberampere. Inductors have values that typically range from 1 μH (10−6 H) to 20 H. Many inductors have a magnetic core made of iron or ferrite inside the coil, which serves to increase the magnetic field and thus the inductance. Along with capacitors and resistors, inductors are one of the three passive linear circuit elements that make up electronic circuits. Inductors are widely used in alternating current (AC) electronic equipment, particularly in radio equipment. They are used to block AC while allowing DC to pass; inductors designed for this purpose are called chokes. They are also used in electronic filters to separate signals of different frequencies, and in combination with capacitors to make tuned circuits, used to tune radio and TV receivers.
The term inductor seems to come from Heinrich Daniel Ruhmkorff, who called the induction coil he invented in 1851 an inductorium.
Calculating Impedance
Impedance is a complex quantity that measures the overall opposition to the flow of alternating current (AC) in an electrical circuit.
Understanding the Components
- Resistance (R): Directly opposes the flow of current and is measured in ohms (Ω).
- Inductive Reactance (XL): Opposes changes in current due to the inductance of components like coils.
It is calculated as XL = 2Ï€fL, where f is the frequency and L is the inductance. - Capacitive Reactance (XC): Opposes changes in voltage due to the capacitance of components like capacitors. It is calculated as XC = 1 / (2Ï€fC), where f is the frequency and C is the capacitance.
Calculating Impedance in Series Circuits
For components connected in series:
- Only Resistance: If only resistors are present, the total impedance (Z) is equal to the sum of the individual resistances: Z = R1 + R2 + ...
- Resistance and One Reactance: If there is resistance and either inductive or capacitive reactance, use the Pythagorean theorem: Z = √(R² + X²):** Z = √(R² + (XL - XC)²)
Calculating Impedance in Parallel Circuits
For components connected in parallel:
- Only Resistance: 1/Z = 1/R1 + 1/R2 + ...
- Resistance and One Reactance: 1/Z² = 1/R² + 1/X²
- Resistance: 1/Z² = 1/R² + 1/(XL - XC)²
Example: Series RLC Circuit
Given:
- Resistance R = 100 ohms
- Inductance L = 0.1 H
- Capacitance C = 10 µF
- Frequency f = 50 Hz
-
Calculate reactances:
- XL = 2Ï€fL = 31.42 ohms
- XC = 1 / (2Ï€fC) = 318.31 ohms
-
Calculate impedance:
- Z = √(R² + (XL - XC)²) = √(100² + (31.42 - 318.31)²) ≈ 317.85 ohms
Remember: Impedance is a complex quantity that can be represented in rectangular form (Z = R + jX) or polar form (Z = |Z|∠θ).
Transformer
Indispensable Components in Electrical Systems
Transformers are passive electrical components that efficiently transfer electrical energy from one circuit to another without a direct electrical connection. Operating on the principle of electromagnetic induction, transformers play a pivotal role in various applications, including power transmission, audio systems, and telecommunications.
Key Functions:
- Voltage Transformation: Transformers can step up or step down voltage levels, enabling efficient transmission and distribution of electrical power.
- Galvanic Isolation: They provide electrical isolation between circuits, minimizing the risk of electrical shocks and improving safety.
- Signal Coupling: Transformers are used to couple stages of signal-processing circuits, optimizing impedance matching and reducing noise.
Operational Principle:
A transformer consists of a primary winding and a secondary winding, typically wound around a magnetic core. When an alternating current flows through the primary winding, it creates a varying magnetic field. This magnetic field induces a voltage in the secondary winding, proportional to the ratio of turns between the primary and secondary windings.
Types of Transformers:
- Power Transformers: Used in large-scale power grids for efficient transmission and distribution of electricity.
- Audio Transformers: Employed in audio equipment to match impedances between components and reduce noise.
- Pulse Transformers: Designed for high-frequency applications, such as in switching power supplies.
- RF Transformers: Used in radio frequency circuits to match impedances and filter signals.
Applications:
Transformers are indispensable components in a wide range of electrical systems, including:
- Power grids
- Audio equipment
- Telecommunications
- Industrial control systems
- Medical devices
Transformer Equations
Ideal Transformer Equations:
For an ideal transformer, the following equations hold:
- Voltage Ratio: V₂/V₁ = N₂/N₁
- Current Ratio: I₂/I₁ = N₁/N₂
- Power Relationship: P₁ = P₂
Where:
- V₁ and V₂ are the voltages of the primary and secondary windings, respectively.
- I₁ and I₂ are the currents of the primary and secondary windings, respectively.
- N₁ and N₂ are the number of turns in the primary and secondary windings, respectively.
- P₁ and P₂ are the power supplied to the primary and delivered by the secondary, respectively.
Real Transformer Equations:
In a real transformer, there are losses due to factors such as core losses (eddy currents and hysteresis) and copper losses (resistance in the windings). These losses result in deviations from the ideal equations.
- Efficiency: η = (P₂/P₁) * 100%
- Voltage Regulation: VR = (|V₁ - V₂|/V₁) * 100%
where:
- η is the efficiency of the transformer.
- VR is the voltage regulation.
Equivalent Circuit:
A real transformer can be represented by an equivalent circuit consisting of an ideal transformer, a primary resistance (Rp), a core loss resistance (Rc), and a leakage reactance (Xl).
Transistors were considered the invention of the twentieth century that changed electronic circuits forever. A transistor is a semiconductor device used to amplify and switch electronic signals and electrical power.
- Field-effect transistors (FET)
- MOSFET (metal–oxide–semiconductor FET) – by far the most widely manufactured electronic component (also known as MOS transistor)
- CMOS (complementary MOS)
- BiCMOS (bipolar CMOS)
- Other transistors
- Bipolar junction transistor (BJT, or simply "transistor") – NPN or PNP
- Photo transistor – amplified photodetector
- Photo Darlington – amplified photodetector
- Sziklai pair (compound transistor, complementary Darlington)
- Tetrode transistor – is any transistor having four active terminals.
- Silicon-controlled rectifier (SCR) – passes current only after triggered by a sufficient control voltage on its gate.
- TRIAC (TRIode for Alternating Current) – bidirectional SCR
- Unijunction transistor (UJT)
- Programmable Unijunction transistor (PUT)
- SITh (static induction thyristor)
Conduct electricity easily in one direction, among more specific behaviours.
- Diode, rectifier, diode bridge
- Schottky diode (hot carrier diode) – super fast diode with lower forward voltage drop
- Zener diode – allows current to flow "backwards" when a specific set voltage is reached.
- Transient voltage suppression diode (TVS), unipolar or bipolar – used to absorb high-voltage spikes
- Varicap, tuning diode, varactor, variable capacitance diode – a diode whose AC capacitance varies according to the DC voltage applied.
- Laser diode
- Light-emitting diode (LED) – a diode that emits light
- Photodiode – passes current in proportion to incident light
- Avalanche photodiode – photodiode with internal gain
- Solar Cell, photovoltaic cell, PV arrays or panels – produce power from light
- DIAC (diode for alternating current), Trigger Diode, SIDAC) – often used to trigger an SCR
- Constant-current diode
- Step recovery diode
- Tunnel diode - very fast diode based on quantum mechanical tunnelling
Diodes are often marked with various codes or symbols to identify their type, value, and other characteristics. These markings can include:
- Coloured Bands or Dots: Similar to resistors, some diodes may have coloured bands or dots that represent specific values or characteristics. The meaning of these colours can vary depending on the manufacturer and diode type.
- Alphanumeric Codes: Many diodes are marked with a combination of letters and numbers, such as "1N4001" or "2N2222A." These codes often follow specific numbering systems like JEDEC or Pro-Electron, which provide information about the diode's type, application, and specifications.
- Silkscreen Markings: Modern diodes frequently have their part number or identification code printed directly on the device's casing using silkscreen technology.
Interpreting Diode Markings:
To interpret diode markings accurately, you may need to consult the manufacturer's datasheet or refer to online resources. The specific meaning of the markings can vary depending on the diode type and manufacturer. However, some general guidelines apply:
- JEDEC Codes: The "1N" prefix in JEDEC codes typically indicates a general-purpose diode. The subsequent numbers provide information about the device's characteristics, such as voltage rating or current capacity.
- Pro-Electron Codes: Pro-Electron codes often use a combination of letters and numbers to convey more specific information about the diode's type, application, and electrical parameters.
- Colour Codes: While colour codes can vary, they often follow similar patterns to resistor colour codes. The first two colours may represent the significant digits of the diode's voltage rating or current capacity, while the third colour indicates the multiplier.
Additional Tips:
- Manufacturer's Datasheet: Always consult the manufacturer's datasheet for the most accurate and up-to-date information on a specific diode's markings and characteristics.
- Online Resources: Websites and forums dedicated to electronics can provide valuable information and resources for interpreting diode markings.
- Diode Tester: If you have access to a diode tester, you can use it to measure the diode's forward voltage drop and reverse leakage current, which can help confirm its identity.
Integrated circuits (ICs), also known as microchips or computer chips, are miniature electronic devices consisting of interconnected components like transistors, resistors, and capacitors. These components are etched onto a small piece of semiconductor material, typically silicon.
ICs have revolutionized electronics by enabling device miniaturization, enhanced functionality, and reduced costs. They are used in a wide range of applications, including computers, smartphones, televisions, and countless other devices.
Key Advantages of Integrated Circuits:
- Miniaturization: ICs are significantly smaller than circuits built from discrete components, allowing for compact and portable devices.
- Reduced Cost: Mass production of ICs using photolithography techniques lowers manufacturing costs, making electronic devices more affordable.
- Enhanced Performance: The close proximity of components in ICs enables faster switching speeds and lower power consumption.
Types of Integrated Circuits:
- General-Purpose ICs: Provide versatile functionality for a wide range of applications.
- Application-Specific Integrated Circuits (ASICs): Designed for specific tasks, offering optimized performance and efficiency.
- System-on-a-Chip (SoC): Integrate multiple subsystems, such as a processor, memory, and peripherals, onto a single chip.
- Field-Programmable Gate Arrays (FPGAs): Configurable ICs that can be programmed to perform various functions.
IC Design and Fabrication:
Designing and fabricating ICs involves complex processes, including:
- Circuit Design: Creating the electrical schematic of the IC.
- Layout: Arranging the components on the silicon substrate.
- Fabrication: Using photolithography techniques to etch the circuit patterns onto the semiconductor material.
Impact on Technology:
Integrated circuits have been instrumental in driving technological advancements. They have enabled the development of powerful computers, smartphones, and other devices that have transformed our lives. The miniaturization and cost reduction made possible by ICs have led to the widespread adoption of electronics in various industries, from healthcare to entertainment.
Electronic Circuit Calculations
Electronic circuit calculations involve determining the behaviour of circuits based on the values of their components and the applied voltage or current. These calculations often involve applying Ohm's Law, Kirchhoff's Laws, and the concepts of impedance and reactance.
Fundamental Concepts:
- Ohm's Law: Relates voltage, current, and resistance: V = IR.
- Kirchhoff's Voltage Law (KVL): The sum of the voltages around any closed loop in a circuit must equal zero.
- Kirchhoff's Current Law (KCL): The sum of the currents entering a node must equal the sum of the currents leaving the node.
- Impedance: The total opposition to the flow of alternating current (AC) in a circuit. It combines resistance, inductive reactance, and capacitive reactance.
- Reactance: The opposition to the flow of AC due to inductance or capacitance.
Common Calculations:
-
Series Circuits:
- Total Resistance: R_total = R1 + R2 + ...
- Total Current: I = V / R_total
- Voltage Drop Across Each Resistor: V_R = IR
-
Parallel Circuits:
- Total Resistance: 1/R_total = 1/R1 + 1/R2 + ...
- Total Current: I_total = I1 + I2 + ...
- Current Through Each Resistor: I_R = V / R
-
RLC Circuits:
- Impedance: Z = √(R² + (XL - XC)²)
- Current: I = V / Z
- Phase Angle: θ = arctan((XL - XC) / R)
-
Power Calculations:
- Power (P): P = VI = I²R = V²/R
- Reactive Power (Q): Q = I²X
- Apparent Power (S): S = √(P² + Q²)
- Power Factor (PF): PF = P / S
Example: A Series Circuit
Consider a series circuit with a 100-ohm resistor, a 0.1 H inductor, and a 10 µF capacitor connected to a 120V, 60 Hz AC source.
-
Calculate reactances:
- XL = 2Ï€fL = 37.7 ohms
- XC = 1 / (2Ï€fC) = 265.26 ohms
-
Calculate impedance:
- Z = √(R² + (XL - XC)²) = 227.8 ohms
-
Calculate current:
- I = V / Z = 120V / 227.8 ohms ≈ 0.526 A
Basic troubleshooting
Calculating Fuse Blowing: A Basic Example
Understanding Fuse Blowing
A fuse is a protective device designed to interrupt a circuit when the current exceeds a predetermined value. This prevents potential damage to electrical equipment and reduces the risk of fire.
Calculating Fuse Blowing
To determine if a fuse will blow, we typically compare the expected current in the circuit to the fuse's rated current. If the expected current exceeds the fuse's rating, the fuse will likely blow.
Example:
Let's consider a simple circuit with a 12V battery, a 10-ohm resistor, and a 5-amp fuse.
- Calculate the expected current: Using Ohm's Law, I = V / R = 12V / 10 ohms = 1.2 A.
- Compare with fuse rating: Since the expected current (1.2 A) is less than the fuse rating (5 A), the fuse will not blow under normal operating conditions.
Factors Affecting Fuse Blowing:
- Fuse Rating: The fuse's amperage rating determines the maximum current it can safely handle before blowing.
- Circuit Load: The amount of current drawn by the connected devices will affect whether the fuse blows.
- Overload Conditions: If the circuit experiences an overload (e.g., due to a short circuit), the current can exceed the fuse rating, causing it to blow.
- Fuse Type: Different types of fuses (e.g., glass, ceramic, blade) have varying characteristics and may blow at slightly different currents.
Note: This is a simplified example. In real-world scenarios, other factors such as ambient temperature, voltage fluctuations, and the specific characteristics of the fuse can influence its behaviour. For more complex calculations or specific applications, consulting electrical engineering references or using specialized software is recommended.
How to use a multimeter
Understand your multimeter, range, functionality, area of usage, etc .. and make sure you have selected the correct range before performing a measuring test. Be causations while testing on High Voltage do not blow up your costly multimeter and risk yourself be electrocuted. Always learn from low-voltage DC if you are a beginner in this exciting field. Always read your instruction manual that comes along with your multimeter to make sure of safety and not damage equipment and your multimeter.
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