What is resistor capacitance? Capacitance is an ability of a body to store electrical energy in the form of electrical charge. Practical resistors always exhibit capacitance as a parasitic property. Depending on the application, resistor capacitance might be easily disregarded, especially in DC circuits. In some applications, such as snubber resistors, the capacitive parasitic effect is actually a desirable effect. On the other hand, parasitic resistor capacitance can be a significant factor in high-frequency AC applications, creating an unwanted effect. The reason for this is that the impedance of a resistor rises with the applied voltage frequency due to the increase in its reactance. The higher the frequency, the lower the impedance is, which means that the resistor can no longer be observed as a constant element at high frequencies, and becomes a frequency-dependent element. Capacitors and resistors Electrical loads can be divided into two types: real (or resistive) loads and reactive loads. Real loads are used to convert electrical power into heat. An ideal resistor is a purely resistive load, which means that all the electrical power applied to the resistor is dissipated as heat. On the other hand, reactive loads convert electrical power into a magnetic or electric field and temporarily store it before returning it to the rest of the circuit. Reactive loads can be inductive or capacitive. Inductive load store energy in the form of a magnetic field, while capacitive loads store energy in the form of an electric field. The main difference between ideal resistors and ideal capacitors is therefore that resistors dissipate electrical power as heat, while capacitors turn electrical power into an electric field. Ideal resistors have zero reactance and as a result their capacitance is zero as well. Unfortunately, electrical devices are not ideal in practice and even the simplest resistors have [… read more]

## Resistor inductance

What is resistor inductance? Inductance is an electrical property of conductors by which an electrical current passing through the conductor induces an electromotive force in the conductor itself (self-inductance) and other conductors nearby. Since resistors are made of conductive materials, they, too, exhibit inductance as an unwanted, parasitic effect. This effect is especially noticeable if the resistor is made out of wire formed into a coil shape. Depending on the application, resistor inductance might be easily disregarded, especially in DC circuits. However, parasitic resistor inductance can be a significant factor in high-frequency AC applications. The reason for this is that the impedance of a resistor rises with the applied voltage frequency due to the increase in its reactance. Inductors and resistors Electrical loads can be divided into two types: real (or resistive) loads and reactive loads. Real loads are used to convert electrical power into heat. An ideal resistor is a purely resistive load, which means that all the electrical power applied to the resistor is dissipated as heat. On the other hand, reactive loads convert electrical power into a magnetic or electric field and temporarily store it before returning it to the rest of the circuit. Reactive loads can be inductive or capacitive. Inductive load store energy in the form of a magnetic field, while capacitive loads store energy in the form of an electric field. The main difference between ideal resistors and ideal inductors is therefore that resistors dissipate electrical power as heat, while inductors turn electrical power into a magnetic field. Ideal resistors have zero reactance and as a result zero inductance. Unfortunately, electrical devices are not ideal in practice and even the simplest resistors have a slight parasitic inductive reactance. Parasitic inductance Resistors are used when a purely resistive load is required, so inductance is often [… read more]

## Electrical resistivity

What is electrical resistivity? Electrical resistivity is a measure of a material’s property to oppose the flow of electric current. This is expressed in Ohm-meters (Ω⋅m). The symbol of resistivity is usually the Greek letter ρ (rho). A high resistivity means that a material does not conduct well electric charge. Electrical resistivity is defined as the relation between the electrical field inside a material, and the electric current through it as a consequence: in which ρ is the resistivity of the material (Ωm),E is the magnitude of the electrical field in the material (V/m),J is the magnitude of the electric current density in the material (A/m2) If the electrical field (E) through a material is very large and the flow of current (J) very small, it means that the material has a high resistivity. Electrical conductivity is the inversion of resistivity, and is a measure of how well a material conducts electric current: in which σ is the conductivity of the material expressed in Siemens per meter (S/m). In electrical engineering often κ (kappa) is used instead of σ. Electrical Resistance Electrical resistance is expressed in Ohms, and is not the same as resistivity. While resistivity is a material property, resistance is the property of an object. The electrical resistance of a resistor is determined by the combination of the shape and the resistivity of the material. For example, a wirewound resistor with a long, thick wire has a higher resistance then with a shorter and thinner wire. A wirewound resistor made from a material with high resistivity has a higher resistance value then one with a low resistivity. An analogy with a hydraulic system can be made, where water is pumped through a pipe. The longer and thinner the pipe, the higher the resistance will be. A pipe full [… read more]

## Power rating

What is the power rating of a resistor? The power rating of a resistor defines the maximum energy a resistor can (safely) dissipate. As is stated by Joule’s first law, the generated electrical power is related to the voltage and current: When the electrical power equals the dissipated heat (by radiation, convection and conduction), the temperature of the resistor will stabilize. The temperature is not equal across the resistor. The resistor body is slightly hotter than the terminals, with the highest temperature at the center of the body. The higher the rate of heat dissipation to the environment, the lower the temperature rise will be. Larger resistors with a bigger surface area can generally dissipate heat at a higher rate. If the (average) power dissipation is larger than the power rating, the resistor may be damaged. This can have several consequences. The resistance value can shift permanently, the lifetime can significantly be reduced or the component is completely damaged resulting in an open circuit. In extreme cases the excessive power can even cause a fire. Special flameproof resistors are available, that cause a circuit brake before the temperature reaches a dangerous state. Power rating definition The power rating of a resistor defines the maximum energy a resistor can (safely) dissipate. Resistor derating The nominal power rating is defined for a certain ambient temperature in free air. Note that the amount of energy that a resistor in practise can dissipate without causing damage, is strongly dependent on the operating conditions and therefore not equal to the nominal power rating. For example, a higher ambient temperature can significantly reduce the power rating. This effect is referred to as derating. It should be taking into account by the designer. Often the power rating is chosen largely above the electric power. Typically resistors are [… read more]

## Resistor properties

The function of resistors is to oppose the flow of electric current in a circuit. Therefore their primary parameter is the resistance value. The manufacturing tolerance must be adequately chosen for each specific application. The ultimate resistance value may deviate from the specification because of many reasons. One is the temperature coefficient of resistance, or TCR, which is often specified for precision applications. Stability defines the long term variations of the resistance. After a long duration of electric load, the resistance value will not return to its original value. Electric noise appears in every resistor, and is for low-noise amplifying applications of importance. For high frequency applications, the inductance and capacitance properties play a role. Next to the characteristics related to resistance value, the maximum power and voltage can be specified. The maximum power rating is mainly for power electronics important, while resistors in electronic circuit boards mostly never reach the maximum power rating. For high voltage circuits, the maximum rated voltage must be taken into account. The quality of a resistor in terms of durability and reliability is for some applications more important than for others. An overview of the most common resistor properties and characteristics to describe a resistor are detailed below. Low Temperature Coefficient of Resistance (TCR) The TCR is dependent on the resistive material and the resistor construction. The temperature dependence of electrical resistivity is determined by the material: Number of phonons Coefficient of expansion from the material Power rating The power rating indicates the maximum dissipation that the component is capable of. The rated dissipation is normally specified at room temperature and decreases at higher temperatures. This is called derating. Typically from 70°C derating is specified. Above this temperature, it can only utilize a reduced power level. This is illustrated by a derating curve. The [… read more]

## Resistor Noise

What is resistor noise? Noise is an unwanted phenomenon for resistors. For some applications the noise properties are important. Examples are high gain amplifiers, charge amplifiers and low-level signals. Resistor noise is often specified as microvolts noise per volt of applied voltage, for a 1 MHz bandwidth. Thermal noise is the predominant source of noise for resistors. It is dependent on three variables: resistance, temperature and bandwidth. The relation between these three parameters is describes by the formula: Where E is the RMS noise signal in volts, R is the resistance in ohms, k is Boltzmann’s constant, T is the temperature in Kelvin and dF is the bandwidth in Hz. The equation shows that the noise level can be decreased by reducing the resistance, the temperature or the bandwidth. Knowing Boltzmann’s constant, the formula is simplified to: Where E is now the noise voltage in nanovolts, R in kΩ, and dF in kHz. Thermal and current noise There are two types of noise: the thermal noise and the current noise. To understand their principle, they will be discussed in more detail. In all materials, the electrons permanently move. As temperature increases, the movements increase. The vibrations of the electrons cause an electric signal (AC) across the terminals of the component. Because the vibrations are completely random, the electrical signal is noise. This is called thermal noise or Johnson noise. It is the main contributor to noise for resistors. Thermal noise is constant over a wide frequency range. Current noise however, declines when frequency is increased. The thermal noise increases with a larger resistance value, while the current noise decreases. Noise standards The way to measure resistor current noise is defined in norm IEC 60195. This makes the comparison of different manufacturers possible. The current noise of a resistor is described [… read more]

## Temperature Coefficient of Resistance

Resistance changes with temperature The temperature coefficient of resistance, or TCR, is one of the main used parameters to characterize a resistor. The TCR defines the change in resistance as a function of the ambient temperature. The common way to express the TCR is in ppm/°C, which stands for parts per million per centigrade degree. The temperature coefficient of resistance is calculated as follows: Where TCR is in ppm/°C, R1 is in ohms at room temperature, R2 is resistance at operating temperature in ohms, T1 is the room temperature in °C and T2 is the operating temperature in °C. Often instead of TCR, α is used. Positive or Negative Temperature Coefficient of Resistance? Resistors are available with a TCR that is negative, positive, or stable over a certain temperature range. Choosing the right resistor could prevent the need for temperature compensation. In some applications it is desired to have a large TCR, for example to measure temperature. Resistors for these applications are called thermistors, and can have a positive (PTC) or negative temperature coefficient (NTC). Measuring methods for the TCR The temperature coefficient of resistance for a resistor is determined by measuring the resistances values over an appropriate temperature range. The TCR is calculated as the average slope of the resistance value over this interval. This is accurate for linear relations, since the TCR is constant at every temperature. However, many materials have a non linear coefficient. For Nichrome for example, a popular alloy for resistors, the relation between temperature and TCR is not linear. Because the TCR is calculated as average slope, it is therefore very important to specify the TCR as well as the temperature interval. The way to measure TCR is standardized in MIL-STD-202 Method 304. With this method, TCR is calculated for the range between [… read more]

## Kirchhoff law

Kirchhoff laws are essential for resistor network theory. They were formulated by the German scientist Gustav Kirchhoff in 1845. The laws describe the conservation of energy and charge in electrical networks. They are also called Kirchhoff’s circuit laws. Kirchhoff contributed also to other fields of science, therefore the generic term Kirchhoff law can have different meanings. Both circuit laws, the Kirchhoff Current Law (KCL) and the Kirchhoff Voltage Law (KVL), will be explained in detail. Kirchhoff Current Law (KCL) The Kirchhoff Current Law (KCL) states that the sum of all currents leaving a node in any electrical network is always equal to zero. It is based on the principle of conservation of electric charge. The law is also referred to as Kirchhoff’s first law. In formula form this is given by: The KCL is easier to understand with an example. Look at an arbitrary “node A” from a resistor network. Three branches are connected to this node. Two of the currents are known: I1 is 2 amperes and I2 is 4 amperes. The current law states that the sum of I1, I2 and I3 must be zero: Kirchhoff Voltage Law (KVL) The second law is also called Kirchhoff’s voltage law (KVL). It states that the sum of the voltage rises and voltage drops over all elements in a closed loop is equal to zero. In formula form: Let’s take an example to explain the second law. Consider a part of a resistor network with an internal closed loop, as shown in the picture below. We want to know the voltage drop between node B and C (VBC). The sum of voltage drops in the loop ABCD must be zero, so we can write: The two circuit laws are explained in the video below. Kirchhoff law example The Kirchhoff laws form [… read more]

## Resistance of a resistor

Resistance of a resistor The function of a resistor is to oppose the electric current through it. This is called electrical resistance, and is measured in the unit ohm. The resistance can be calculated with Ohms law, when the current is known and the voltage drop is measured: The resistance of a resistor is dependent on its material and shape. Some materials have a higher resistivity, causing a higher value. The value is often printed on the resistor with a number or in the form of a color code. What is resistance? The concept of current, voltage and resistance can be explained by a hydraulic analogy. A flow of water through a pipe is restricted by a constriction. This causes a pressure drop after the constriction. The flow of water is equivalent to electric current. The pressure drop is equal to the voltage drop. The constriction is equivalent to the resistor, and has a certain resistance. The resistance is proportional to the voltage or pressure drop for a given current. In the hydraulic example, the resistance can be increased by for example reducing the diameter of the constriction. For a resistor or wire, the resistance is in general dependent on the material and the geometrical shape. The influence of the geometrical shape, can easily be explained by using the hydraulic example. A long and narrow tube will have a higher resistance than a short and wide tube. The resistance property of a material is called resistivity. The electrical resistance of a resistor is proportional to the resistivity of the material. For a rectangular cross-section resistor the resistance R is given by: where ρ is the resistivity of the resistor material (W·m), l is the length of the resistor along direction of current flow (m), and A is the [… read more]

## Ohm’s law

What is Ohm’s law? Ohm’s law states that the electrical current through a conductor is proportional to the potential difference across it. Furthermore, the electrical resistance of the conductor is constant. This leads to the mathematical equation: where I is the current in amperes, V the voltage in volts and R the resistance in ohms. To illustrate: a resistor of one ohm subjected to a current of 1A has a voltage difference of 1V across its terminals. The equation is named after Georg Ohm. In 1827 he published his findings that form the basis of the formula that is used today. He performed a large series of experiments that showed the relation between applied voltage and current through a conductor. The law is therefore empirical. Although Ohm’s law is one of the fundamentals of electrical engineering, at the time of publication it was received with criticism. The ohm is adopted as the official SI unit for electrical resistance. Gustav Kirchhoff (known from Kirchhoff’s circuit laws) made a generalization that is more used in physics: where σ is the conductivity parameter (material specific), J is the current density in a location of that material, and E the electric field in that location. Ohm’s law and resistors Resistors are passive elements that introduce resistance to the flow of electric current in a circuit. A resistor that functions according to Ohm’s law is called an Ohmic resistor. When current passes through an Ohmic resistor, the voltage drop across the terminals is proportionally to the magnitude of resistance. Ohm’s formula stays also valid for circuits with varying voltage or current, so it can be used for AC circuits as well. For capacitors and inductors the law can of course not be used, since their I-V curve is inherently not linear (not Ohmic). Ohm’s formula [… read more]