Lesson 3. Resistance (resistance or resistor)
Higher category : [Circuit Theory] Circuit Theory Index
1. Characteristics of Resistance
2. Ohm’s Law
3. Types of Resistance
4. Color Coding
5. Relationship Between Resistance and Temperature
6. Various Resistance Values
7. Surface Resistance
8. Measurement of Resistance
1. Characteristics of Resistance
⑴ Power always has a positive sign : The direction of the electric field and the direction of the current are always the same.
⑵ The resistance of all resistors is positive : However, theoretically, resistance can also be considered negative.
① Example : TR, equivalent circuit resistance
⑶ Resistance and Conductance
① Resistance (Unit : Ω) : Degree to which it impedes the flow of current
② Conductance (Unit : ℧ or S (siemens)) : Degree to which it allows current to flow
○ (Note) In AC resistance, conductance is the real part of admittance
2. Ohm’s Law
⑴ Established experimentally by German scientist Georg Simon Ohm in 1827
⑵ Law: Approximately valid in Ohmic materials
⑶ Proof
① m : Mass of electrons
② q : Charge of electrons (C) (considering the sign)
③ μ : Collision frequency (Hz)
④ J : Current density
⑤ σ : Electrical conductivity (㎡)
⑥ E : Electric field (N/C)
⑦ N : Electron density
⑧ For copper commonly used in wires, the time constant τ = 1 / μ = 10^-14, so the term e^-μt can be neglected, leading to the following approximation
○ J(τ) = 0.632 J(∞)
○ J(3τ) = 0.95 J(∞)
○ J(5τ) = 0.99 J(∞)
⑨ The following approximately holds in Ohmic materials
○ σ : Conductivity
○ ρ : Resistivity. The reciprocal of σ
⑷ Time-Current Density Curve of Ohmic Materials
Figure 1. Time-Current Density Curve of Ohmic Materials
① Near t = 0, current linearly increases due to time constant = 1/μ
② After sufficient time, stabilizes at a specific value
3. Types of Resistance
⑴ Fixed resistance : Resistance value does not change
① Lead type : Carbon-composition
○ Finely ground carbon, non-conductive filler, combined with synthetic resin adhesive
○ Ratio of carbon to non-conductive filler determines resistance value
○ Low power ratings : 2 W, 1 W, 0.5 W, 0.25 W, 0.125 W
Figure 2. Lead type : Carbon-composition
② Lead type : Film resistor
○ 1st. Ceramic rod surrounded by carbon film or metal film (Nickel-Chromium) (film acts as resistance)
○ 2nd. Filmed ceramic rod is spiral-cut to achieve desired resistance value
○ Precise control over desired resistance value
Figure 3. Lead type : Film resistor
③ Lead type : Wire wound resistor
○ Wire wound around insulating rod, sealed with additional insulation
○ High conductivity and power handling capacity
○ Not suitable for high-frequency power sources
○ Second image’s corrugated structure dissipates heat
Figure 4. Lead type : Wire wound resistor
④ Resistor network : Modified form of lead type
Figure 5. Resistor network
⑤ Tiny chip resistor
Surface Mount Device (SMD) for Small Circuits: Suitable for constructing small circuits.
Chip Resistor on Ceramic Substrate: Resistance determined by height ratio.
Figure 6. Tiny Chip Resistor
⑵ Variable Resistor (Rheostat): Resistor whose value can be changed.
① Notation
② Type 1: Potentiometer: Device to adjust resistance length. Used for linear or angular displacement measurements.
Notation and Structure of Potentiometer
Figure 7. Notation and Structure of Potentiometer
Using Potentiometer as a Variable Resistor
Figure 8. Using Potentiometer as a Variable Resistor
Types of Potentiometers
Figure 9. Types of Potentiometers
③ Type 2: Tachometer: Used to measure angular velocity.
Structure of Tachometer
Figure 10. Structure of Tachometer
Principle: Measuring angular velocity through electromagnetic induction.
④ Type 3: Linear Variable Differential Transformer (LVDT)
Used for larger displacement measurements.
Suitable for continuous variations in displacement.
Current pattern in coils varies based on magnet position within the coil.
⑤ Type 4: Accelerometer
Old Structure: Mechanical sensor.
Modern Structure: Semiconductor + piezoelectric material.
⑥ Type 5: Bolometer
Absorbs incident infrared radiation, leading to temperature increase and resistance change in the object.
5-1. Metallic: Metal wires like platinum or nickel (RTD, Resistance Temperature Diode).
5-2. Semiconductor: Thermistors, silicon, etc.
5-3. Superconductor(semiconductor).
⑦ Type 6: Thermistor
Definition: Semiconductor variable resistor whose value changes automatically with temperature.
Kitasato Shibasaburo: Produced the world’s first thermistor thermometer.
Temperature Coefficient: Positive when resistance increases with temperature, negative when resistance decreases.
Type 1: NTC Thermistor: Resistance decreases with temperature increase, most commonly used due to ease of manufacture.
Type 2: PTC Thermistor: Resistance increases with temperature increase.
Figure 11. NTC and PTC
Arduino Kit’s Thermistor: Resistance of 100 kΩ at 25 ℃.
(Note) Resistance changes in materials with temperature.
Figure 12. Resistance Changes in Conductors, Semiconductors, and Insulators with Temperature
Conductors: Resistance increases with temperature due to increased atomic vibrations.
Semiconductors: Resistance decreases with temperature due to increased carriers.
Insulators: Resistance decreases with temperature as electrons separate from atoms.
(Note) Resistance decrease effect in semiconductors and insulators is stronger than resistance increase effect due to increased atomic vibrations.
(Note) Components like computer parts using semiconductors induce overcurrent with temperature increase, hence the need for cooling systems.
Steinhart Equation: Experimental formula for thermistor resistance changes with temperature.
T: Absolute temperature.
T0: 298.15 K.
R0: Resistance value at 25 ℃. Commonly 100 Ω, 500 Ω, 1 kΩ, 4.7 kΩ, 10 kΩ, 47 kΩ, 100 kΩ.
R: Measured resistance.
B: Temperature coefficient. Commonly 3950 for 10 kΩ.
Alternative Steinhart Equation
Example: Mainly using semiconductors.
Example 1: Sintered metal oxide: Mixture of metal oxides, chromium, cobalt, iron, manganese, nickel.
Example 2: Doped polycrystalline ceramic: Includes BaTiO3.
⑧ Type 7: Photoconductive Cell
Definition: Variable resistor with resistance changing automatically with light intensity. No polarity.
Notation: Sometimes represented as λ.
Figure 13. Notation of Photoconductive Cell
Photoconductance Coefficient: Negative value results in resistance decrease with increasing light intensity.
Generally, semiconductor materials that decrease in electrical resistance upon absorbing light are used.
1st. Illuminating light generates electron-hole pairs in the near-infrared range (750 nm ~ 3000 nm).
2nd. Photoconductive effect: Increases the electrical conductivity of regions where electron-hole pairs are generated.
3rd. Increased electrical conductivity leads to increased current.
4th. Measuring the change in current allows detection of light intensity.
Examples: CdS, CdSe, PbS, PbSe (800 nm ~ 2000 nm), Ge:Au, HgCdTe, Hg1-xCdxTe.
Example: Cadmium Sulfide Cell (CdS cell)
Figure 14. Cadmium Sulfide Cell
Advantages: High sensitivity, compact, cost-effective, high power capacity, noise-resistant, AC operation possible, relatively large output.
Disadvantages: Slow response time (10 ~ 100 ms), low light characteristics, susceptible to ambient light interference causing significant hysteresis.
Dark Resistance: About 200 kΩ.
Light Intensity Like Theater Seats (10 lux): About 10 kΩ.
Excessive Light: Very low resistance causing overcurrent.
4. Color Coding
⑴ Resistor Value Represented by Color: Small resistors have their values represented by color bands.
⑵ Color Band Positioning: Asymmetric, read from the side closest to the end of the resistor.
⑶ 4-Band Resistor
① Color Code
Figure 15. 4-Band Color Coding
② Two-Digit Numbers, Powers of 10, Tolerance
Table 1. Examples of 4-Band Resistor
⑷ 5-Band Resistor
① Color Code
Figure 16. 5-Band Color Coding
② Three-Digit Numbers, Powers of 10, Tolerance
Table 2. Examples of 5-Band Resistor
⑸ Sometimes, additional notation indicates the likelihood of malfunction after 1000 hours of use in the existing Color Coding.
5. Relationship Between Resistance and Temperature
⑴ General Trend
① Conductors: Resistance increases due to increased atomic vibrations with temperature.
② Semiconductors: Resistance decreases due to increased carriers with temperature increase.
Example: Components like computer parts
using semiconductors induce overcurrent with temperature increase, hence the need for cooling systems.
③ Insulators: Resistance decreases as electrons separate from atoms with temperature increase.
Example: Ceramic heaters require a controller as they are a positive feedback circuit.
Figure 17. Resistance Changes in Conductors, Semiconductors, and Insulators with Temperature
⑵ Ohmic and Non-Ohmic Materials
① Ohmic Material: Substance where resistance doesn’t change with current or voltage.
② Non-Ohmic Material: Substance where resistance changes with current or voltage.
③ No perfect ohmic material; called ohmic within a narrow range approximately.
④ Heat generated by current, increasing temperature changes the slope of I-V curve, turning it into non-ohmic.
⑶ Near-Room-Temperature Carbon-Composition Resistance Changes: Usually, resistance decreases as temperature increases.
Figure 18. Carbon-Composition Resistance Changes near Room Temperature
⑷ Resistance-Temperature Coefficient
① Inferred Absolute Temperature: Extrapolated temperature axis in temperature-resistance graph.
Graph Example
Figure 19. Inferred Absolute Temperature
Used to calculate resistance value at arbitrary temperature.
α20 (Temperature Coefficients of Resistance): Resistance value at 20 ℃.
T_i Example
Table 3. T_i Example
② PRM/℃
R_nominal: Resistance value at room temperature.
△T = T - 20 ℃
6. Various Resistance Values
⑴ Resistivity: The table below indicates resistivity (unit: Ωm) at 300 K.
Table 4. Resistivity
⑵ Standard Resistances: Resistors with standard values.
① Precision Resistor: 1 Ω units, more expensive than standard resistors.
② Examples of Standard Resistances
Table 5. Examples of Standard Resistances
③ Standard Resistance According to Error Range
Examples of Standard Resistance According to Error Range
Table 6. Examples of Standard Resistance According to Error Range
Reason for Nonlinear Standard Resistance Values
Even for the same standard resistance value, there are errors, suggesting finding suitable resistance values.
Producing exact resistance values leads to excessive inventory accumulation.
Figure 20. Distribution of Standard and Actual Resistance Values
⑸ American Wire Gauge (AWG): Standard for wire thickness.
① Circular Mil (CM): A = d², d unit: mil.
② Square Mil (SM): A = π (0.5 × d)², d unit: mil.
③ Copper Wire AWG Standard
Table 7. Copper Wire AWG Standard
④ Circuit board wires commonly use #22 ~ #24, and wire resistance in experiments is typically a few Ω.
7. Sheet Resistance
⑴ Block-Shaped Resistance Production: Height maintained at a constant level.
⑵ Adjusting Lengths: Adjusting lengths horizontally and vertically to determine resistance, a concept devised in addition to uniform height.
⑶ Formulation (Sheet Resistance is R_s)
8. Resistance Measurement
⑴ Low-Resistance Measurement (Below 1 Ω)
① Kelvin Double Bridge Method: Precise measurement of low resistances (10-5 ~ 1 Ω), coarse spiral wire resistance.
⑵ Medium-Low Resistance Measurement (1 Ω ~ 10 kΩ)
① Voltage and Current Method of Voltage Fall: Used for measuring filament resistance in incandescent bulbs, etc.
② Murray Loop Method (Type of Wheatstone Bridge Method): Thin wire resistance of a few thousand Ω.
⑶ Special Resistance Measurement
① Wheatstone Bridge Method: Internal resistance of galvanometer.
② Kohlrausch Bridge Method: Resistance of electrolytes, grounding resistance.
③ Megger Method: Insulation resistance of outdoor electrical lines.
Input: 2015-12-30 22:54
Modified: 2018-12-11 23:00