Resistance characteristics
Georg Simon Ohm
[1] Relationship between closed-loop power and resistance
The formula R=U/I or U=IR derived from Ohm's law I=U/R cannot be said that the resistance of a conductor is directly proportional to the voltage passing through it and inversely proportional to the current passing through it, because the resistance of a conductor is an attribute of itself, which depends on the length, cross-sectional area, material, temperature and humidity of the conductor (the second stage does not involve humidity). Even if there is no voltage and no current across it, its resistance is a constant value. Generally speaking, this fixed value can be regarded as a constant, because for photoresistors and thermistors, the resistance value is uncertain. For some conductors, superconductivity still exists at a very low temperature, which will affect the resistance value of the resistor and has to be considered. The current in a conductor is directly proportional to the voltage across the conductor and inversely proportional to the resistance of the conductor. (I=U:R)
The unit of resistance
The unit ohm of resistance is abbreviated as ω. 1ω is defined as 1ω when the potential difference between the two ends of the conductor is 1V (ν) and the current passing through it is 1A, its resistance is1ω. formula
Standard formula: R=U/I Ohm's law formula for partial circuits: I=U/R or I = U/R = Gu (I = U: R).
Formula description
Definition: When the voltage is constant, where G= 1/R, the reciprocal g of resistance R is called conductance, and its international unit system is Siemens (S). Among them, I, U and R- are the current intensity, voltage and resistance of the same part of the circuit at the same time.
Ohm's law (20 sheets) I=Q/t current = charge amount/time (all units are in the international system of units), that is, current = voltage/resistance or voltage = resistance × current "can only be used to calculate voltage and resistance, and does not mean that resistance has a changing relationship with voltage or current".
application area
Ohm's law applies to pure resistance circuits, metal conduction and electrolyte conduction, but Ohm's law does not apply to formulas in gas conduction and semiconductor components.
I=E/(R+r)=(Ir+U)/(R+r) I- current ampere (A) E- electromotive voltage (V) R- resistance ohm (ω)R- internal resistance ohm (ω)U- voltage volt (v).
Formula description
Where E is electromotive force, R is external circuit resistance, R is internal resistance of power supply, internal voltage U is equal to IR, and E is equal to internal+external application range of U: it is only suitable for periodic excitation of pure resistance circuits (like household circuits, not pure resistance circuits).
Capacitance, inductance, transmission line, etc. Are reactive components of the circuit. Assuming that a periodic voltage or a periodic current is added to a circuit with reactance elements, the relationship between voltage and current becomes a differential equation. Because the equation of ohm's law only involves real resistance, but not complex impedance which may contain capacitance or inductance, the above ohm's law cannot be directly applied to this situation. The most basic periodic excitation, such as sine excitation or cosine excitation, can be expressed by exponential function:
Where j is the imaginary part, ω is the real angular frequency and t is the time. It is assumed that the periodic excitation is a single-frequency sinusoidal excitation with an angular frequency ω. The resistance impedance of resistance R is z = R, the inductance impedance of inductance L is z = j ω l, the capacitance impedance of capacitance C is z = 1/j ω c, and the relationship between voltage V and current I is V= IZ. Note that if resistance R is replaced by impedance Z, the ohm's law equation can be generalized. Only the real value part of z will cause the dissipation of thermal energy. For this system, the complex waveforms of current and voltage are I = i0e j ω t and V = v0e j ω t, respectively. The real parts of current and voltage, real(I) and real(V), describe the real sinusoidal current and sinusoidal voltage of the circuit respectively. Since I0 and V0 are different complex scalar values, the phases of current and voltage may be different. Periodic excitation can be Fourier decomposed into sine function excitation with different angular frequencies. For sine function excitation of each angular frequency, the above method can be used to calculate the response. Then, add up all the answers and you can get the answer.
Linear approximation
However, some circuit elements do not obey Ohm's law, and the relationship between voltage and current (V-I line) is nonlinear. The PN junction diode is an obvious example. As shown on the right, the current does not increase linearly with the increase of the voltage on the diode. Given the external voltage, the current can be estimated by V-I line, but it can't be calculated by Ohm's law, because the resistance will change with the voltage. In addition, the current will increase significantly only when the external voltage is positive; When the applied voltage is negative, the current is equal to zero. For this kind of components, ohm's law of volt-ampere line slope is one of several basic equations used in circuit analysis. It can be applied to metal conductors or resistors specially prepared for this performance. In electrical engineering, these things are everywhere. A substance or element that obeys ohm's law is called "ohm substance" or "ohm element". Theoretically, no matter the applied voltage or current, whether it is DC or AC, whether it is positive or negative, their resistance remains unchanged.
, called "small signal resistance", "incremental resistance" or "dynamic resistance", is defined as
The unit is also ohm, which is a very important resistance and is suitable for calculating the electrical properties of non-ohmic components. Problems needing attention in the study of ohm's law 1. When analyzing the power problem in the closed circuit, we should pay attention to the following three problems: (1) When the current changes, the terminal voltage of this circuit changes, so don't forget this when comparing and calculating the power. (2) Using the conclusion that the output power is maximum when the external resistance is equal to the internal resistance. When necessary, a certain resistance should be regarded as internal resistance and treated as equivalent power supply. (3) Pay attention to which part of the circuit the required power is, and different parts of the circuit have different analysis ideas. (2) In the DC circuit, when the capacitor is charged and discharged, there is charging and discharging current in the circuit. Once the circuit reaches a stable state, the capacitor is equivalent to an element with infinite resistance in the circuit, and the circuit at the capacitor is regarded as an open circuit. When simplifying the circuit, it can be removed. When analyzing and calculating DC circuits with capacitors, we should pay attention to the following points: (1) The voltage between the two plates of the capacitor is equal to the voltage at both ends of the branch. (2) When the capacitor is connected in parallel to the circuit, the voltage between the two plates of the capacitor is equal to the voltage across the parallel electrical apparatus. (3) When the current and voltage of the circuit change, the capacitor will be charged (discharged). If the charged property of the polar plate changes before and after the change, the amount of charge passing through each lead is equal to the sum of the charge of the capacitor in the initial and final state. [2] Equation james maxwell's interpretation of Ohm's Law is that the electromotive force of a conductor in a certain state is directly proportional to the generated current. So the ratio of electromotive force to current, that is, resistance, will not change with current. Here, the electromotive force is the voltage across the conductor. In the context of this reference, the modifier "in a certain state" is interpreted as being in a normal temperature state, because the resistivity of a substance usually depends on the temperature. According to Joule's law, the Joule heat of a conductor is related to the current. When current is conducted to a conductor, the temperature of the conductor will change. The dependence of resistance on temperature makes the resistance depend on current in typical experiments, so it is not easy to directly test this form of ohm's law. 1876, Maxwell and his colleagues, * * *, designed several experimental methods to test ohm's law, which can particularly highlight the response of electrical conductors to thermal effects.