Keith Mack
Ohm's law states that the voltage difference across a resistor is proportional to the current through the resistor. The constant of proportionality is the resistance, R. The law can be written as a mathematical equation, with the units of resistance being ohms (Ω). While this law holds true for most materials, there are some electrical circuit components that do not obey Ohm's law. These components exhibit negative resistance, where the current and voltage are inversely proportional to each other. This behaviour can be observed in certain nonlinear (nonohmic) devices, where the I-V curve is not a straight line. This raises the question: can Ohm's law be negative?
| Characteristics | Values |
|---|---|
| Ohm's Law | The voltage difference across a resistor is proportional to the current through the resistor. |
| Resistance | The constant of proportionality. |
| Ohm's Law in Negative Resistance | Ohm's law does not apply to negative resistance as the resistance is not constant. |
| Negative Resistance | A behaviour in which the current and voltage are inversely proportional to each other. |
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What You'll Learn
Ohm's Law and negative resistance
Ohm's law states that the voltage difference across a resistor is directly proportional to the current through the resistor. The constant of proportionality is the resistance, R. Mathematically, this is represented as v(t) = i(t) * R, where v(t) is the voltage across the resistor and i(t) is the current through the resistor.
Negative resistance is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is contrary to the behaviour of an ordinary resistor, where an increase in voltage leads to a proportional increase in current, as described by Ohm's law. In other words, negative resistance occurs when the applied voltage and measured current are inversely proportional, defying Ohm's law.
Negative resistance is an uncommon property exhibited by a few nonlinear electronic components. It is characterised by a negative slope in the current-voltage (I-V) curve, indicating a decrease in current with increasing voltage. This behaviour can be observed in certain devices, such as tunnel diodes, Gunn diodes, and gas discharge tubes like neon lamps and fluorescent lights. These devices are considered active resistors and can amplify signals, even with just two terminals.
Despite the name, negative resistance does not imply a negative value of resistance in the context of Ohm's law. Instead, it refers to a negative value of the differential resistance, which is the ratio of the change in voltage to the resulting change in current (Δv/Δi). This negative differential resistance can be utilised in electronic oscillators, amplifiers, and switching circuits, especially at microwave frequencies.
In summary, negative resistance describes a phenomenon where an increase in voltage leads to a decrease in current, contrary to the behaviour predicted by Ohm's law. This unique property has valuable applications in electronics, particularly in signal amplification and oscillatory circuits.
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Nonlinear devices and negative resistance
Ohm's law states that the voltage difference across a resistor is directly proportional to the current through the resistor. The constant of proportionality is the resistance, R. Mathematically, this is represented as:
$$v(t) = R \cdot (t)$$
$$i(t) = v(t) / R$$
$$R = v(t) / i(t)$$
Where:
- V(t) is the voltage across the resistor
- I(t) is the current through the resistor
- R is the resistance of the conductor
Ohm's law is an empirical relation that accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However, there are some electrical components that do not obey Ohm's law. These components exhibit nonlinear or non-ohmic behaviour, meaning their relationship between current and voltage (I-V curve) is not a straight line through the origin.
One example of a nonlinear device is the p-n junction diode. In this case, the current does not increase linearly with the applied voltage. While a value of current (I) can be determined for a given value of applied voltage (V) from the I-V curve, it cannot be determined from Ohm's law because the resistance is not constant.
Another example of a nonlinear device is the varistor, which is specifically engineered to provide a nonlinear resistance curve. Commonly made from compounds such as zinc oxide or silicon carbide, varistors maintain high resistance across their terminals until a certain "firing" or "breakdown" voltage is reached, at which point their resistance decreases significantly.
Negative resistance is an uncommon property exhibited by some nonlinear electronic components. Unlike positive resistance, negative resistance varies with the voltage or current applied to the device. Devices with negative resistance can only exhibit this property over a limited portion of their voltage or current range. Negative resistance occurs when the slope of the current-voltage curve is negative, meaning the current decreases as the applied voltage increases. Examples of devices that can exhibit negative resistance include high-vacuum electron tubes (tetrodes) and semiconductor diodes (Esaki or
Negative resistance devices have several applications. They are used in electronic oscillators and amplifiers, particularly at microwave frequencies. Negative resistance devices can also be used in switching circuits, where they can abruptly change from one state to another with hysteresis. For example, a relaxation oscillator, flip-flop, or memory cell can be built using a single active negative resistance device, whereas two active devices (transistors) would be required using standard logic circuits.
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Ohm's Law and negative voltage
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. The law was named after German physicist Georg Ohm, who, in an 1827 treatise, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. The first and perhaps most important relationship between current, voltage, and resistance is called Ohm's Law.
Ohm's law can be written as three mathematical equations:
- V = IR
- I = V/R
- R = V/I
Where:
- I is the current through the conductor
- V is the voltage measured across the conductor
- R is the resistance of the conductor
The units of resistance are ohms (Ω), with thousands of ohms represented as kilo-ohms (kΩ) and millions of ohms represented as mega-ohms (MΩ). Voltage is measured in volts, symbolized by the letters "E" or "V", while current is measured in amps, symbolized by the letter "I".
Ohm's law is an empirical relation that accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. It has been observed on a wide range of length scales, from early 20th-century experiments at the atomic scale to modern research on ultra-thin silicon wires.
It is important to note that Ohm's law assumes a constant resistance, and if the resistance is not constant, the equation cannot be used as Ohm's law, but it can still define static/DC resistance. Additionally, there are components of electrical circuits that do not obey Ohm's law, exhibiting a nonlinear or non-ohmic relationship between current and voltage. An example is the p-n junction diode, where the current does not increase linearly with applied voltage, and the current only increases significantly if the applied voltage is positive, not negative.
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Ohm's Law and negative current
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. The law can be mathematically represented as:
$$V(t) = R \cdot (t)$$
$$I(t) = V(t) * R$$
$$R = V(t)/I(t)$$
Where V(t) is the voltage across the resistor, i(t) is the current through the resistor, and R is the resistance. The units of resistance are ohms, abbreviated as Ω.
Ohm's law is an empirical relation that accurately describes the conductivity of the vast majority of electrically conductive materials over a wide range of current magnitudes. It is one of the most basic and important laws of electric circuits.
However, it is important to note that Ohm's law has its limitations. It does not apply to all electrical circuits or components. For example, the filament of a light bulb violates Ohm's law because increasing the current also increases the temperature, which, in turn, affects the current.
Additionally, there are electrical circuits with components that do not obey Ohm's law, exhibiting a nonlinear or non-ohmic relationship between current and voltage. An example is the p-n junction diode, where the current does not increase linearly with the applied voltage. In such cases, Ohm's law cannot be used to determine the current for a given value of applied voltage, as the resistance is not constant.
Regarding negative values in Ohm's law, it is important to consider the direction of the current relative to the sign of the voltage difference. In a typical battery, electric current moves from the positive terminal to the negative terminal. Therefore, the direction of the current and the sign of the voltage difference are essential considerations when analyzing circuits using Ohm's law.
In summary, Ohm's law describes the relationship between voltage, current, and resistance in electrical circuits, but it has limitations and does not apply to all circuit components. The direction of the current and voltage polarity are crucial factors to consider when applying Ohm's law, and negative values may indicate a reversal in the expected current direction or a violation of the law in certain components.
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Ohm's Law and negative temperature
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. The constant of proportionality, the resistance, can be introduced to arrive at the three mathematical equations used to describe this relationship. The law is expressed as:
$$ I = \frac{V}{R}$$
$$ V = IR$$
$$ R = \frac{V}{I}$$
Where:
- I is the current through the conductor
- V is the voltage measured across the conductor
- R is the resistance of the conductor
Ohm's law is foundational in the field of electronics and thermal systems. It has been used to improve the efficiency of thermal systems using power and temperature controllers. The law is also crucial in troubleshooting thermal systems. For instance, if there is a fluctuation in the electrical current or heat output, Ohm's law can be used to validate the static values of circuit components and identify voltage measurements across components.
Ohm's law is valid only at a constant temperature. The dependence of resistance on temperature makes it challenging to directly verify the law in its original form. The discovery of Johnson-Nyquist noise in the 1920s revealed that the current through a practical resistor has statistical fluctuations that depend on temperature, even when voltage and resistance remain constant. This thermal effect implies that measurements of current and voltage taken over short periods will yield V/I ratios that deviate from the expected value of R.
While the law is not considered universal, it remains applicable to a wide range of length scales. It has been observed to hold for silicon wires as small as four atoms wide and one atom high.
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Frequently asked questions
Ohm's Law states that the voltage difference across a resistor is directly proportional to the current through the resistor. The constant of proportionality is the resistance, R.
Ohm's Law can be negative in certain cases. Negative resistance occurs in a few non-linear (non-ohmic) devices where the I-V curve is not a straight line, so it does not obey Ohm's Law. In these cases, the resistance is not constant and varies with the voltage or current.
Negative resistance is an uncommon property exhibited by some non-linear electronic components. In these components, the current increases when the voltage decreases, which is the opposite of a normal circuit with a resistor following Ohm's Law.
Negative resistance can be observed in certain circuits with amplifying devices like transistors or op-amps. It can also be emulated through clever circuitry, although it is limited to a specific voltage and current range.
