Who did not study physics at school? For some, it was interesting and understandable, while someone pored over textbooks, trying to memorize complex concepts. But each of us remembered that the world is based on physical knowledge. Today we will talk about concepts such as current inductance, circuit inductance, and find out what capacitors are and what a solenoid is.
Electrical circuit and inductance
Inductance serves to characterize the magnetic properties of an electrical circuit. It is defined as the coefficient of proportionality between the current electric current and magnetic flux in a closed loop. The flow is created by this current through the surface of the circuit. Another definition says that inductance is a parameter of an electric circuit and determines the emf of self-induction. The term is used to indicate a chain element and is a characteristic of the self-induction effect, which was discovered by D. Henry and M. Faraday independently of each other. Inductance is associated with the shape, size of the circuit and the value of the magnetic permeability of the environment. In SI units, this value is measured in Henry and is denoted as L.
Self Induction and Inductance Measurement
Inductance is a value that is equal to the ratio of the magnetic flux passing through all the turns of the circuit to the current strength:
The inductance of the circuit depends on the shape, size of the circuit and on the magnetic properties of the medium in which it is located. If an electric current flows in a closed circuit, then a changing magnetic field arises. This will subsequently lead to the emergence of EMF. The creation of an induction current in a closed loop is called "self-induction." According to the Lenz rule, the value does not allow the current in the circuit to change. If self-induction is detected, an electrical circuit can be used in which a resistor and an iron core coil are connected in parallel. Electric lamps are connected in series with them. In this case, the resistance of the resistor is equal to the DC resistance of the coil. The result is a bright burning lamp. The phenomenon of self-induction occupies one of the main places in radio engineering and electrical engineering.
How to find inductance
The formula, which is the simplest to find the quantity, is as follows:
where F is the magnetic flux, I is the current in the circuit.
Through inductance, the emf of self-induction can be expressed:
From the formula, a conclusion is drawn about the numerical equality of induction with EMF, which occurs in the circuit when the current strength changes by one ammeter in one second.
Variable inductance makes it possible to find the energy of the magnetic field:
"Spool of thread"
The inductor is a coiled insulated copper wire on a solid base. As for insulation, the choice of material is wide - it is varnish, and wire insulation, and fabric. The magnitude of the magnetic flux depends on the area of the cylinder. If you increase the current in the coil, then the magnetic field will become more and more and vice versa.
If an electric current is supplied to the coil, then a voltage opposite to the voltage will appear in it, but it suddenly disappears. This kind of voltage is called the electromotive force of self-induction. At the moment of switching on the voltage to the coil, the current strength changes its value from 0 to a certain number. The voltage at this moment also changes value, according to Ohm's law:
where I is the current strength, U is the voltage, R is the resistance of the coil.
Another special feature of the coil is the following fact: if you open the circuit "coil - current source", then the EMF will be added to the voltage. Current will also rise at first, and then decline. This implies the first law of switching, which states that the current strength in the inductor does not instantly change.
The coil can be divided into two types:
- With magnetic tip. Ferrites and iron act as the material of the heart. Cores serve to increase inductance.
- With non-magnetic. Used in cases where the inductance is not more than five milliHenry.
Devices differ in appearance and internal structure. Depending on such parameters, the inductance of the coil is found. The formula in each case is different. For example, for a single-layer coil, the inductance will be equal to:
- L = 10µ0ΠN 2 R 2 : 9R + 10l.
And here is another formula for a multilayer:
- L = µ0N 2 R 2 : 2Π (6R + 9l + 10w).
Key findings related to coil operation:
- On cylindrical ferrite, the largest inductance occurs in the middle.
- To obtain maximum inductance, it is necessary to wind the coils close to the coil.
- Inductance is less, the smaller the number of turns.
- In the toroidal core, the distance between the turns does not play the role of a coil.
- The inductance value depends on the "turns in a squared".
- If inductances are connected in series, then their total value is equal to the sum of inductances.
- When connecting in parallel , make sure that the inductances are spaced on the board. Otherwise, their readings will be incorrect due to the mutual influence of magnetic fields.
Solenoid
This concept refers to a cylindrical winding of a wire that can be wound in one or more layers. The length of the cylinder is much larger than the diameter. Due to this feature, when an electric current is applied to the solenoid cavity, a magnetic field is generated. The rate of change of the magnetic flux is proportional to the change in current. The inductance of the solenoid in this case is calculated as follows:
This type of coil is also called an electromechanical retractable core actuator. In this case, the solenoid is supplied with an external ferromagnetic magnetic circuit - the yoke.
Nowadays, the device can combine hydraulics and electronics. Four models were created on this basis:
- The first is able to control linear pressure.
- The second model differs from others by the forced control of the clutch lock in torque converters.
- The third model contains pressure regulators that are responsible for the work of speed switching.
- The fourth is controlled hydraulically or by valves.
Necessary formulas for calculations
To find the inductance of the solenoid, the formula is applied as follows:
where µ0 shows the magnetic permeability of the vacuum, n is the number of turns, V is the volume of the solenoid.
You can also calculate the inductance of the solenoid using another formula:
where S is the cross-sectional area, and l is the length of the solenoid.
To find the inductance of the solenoid, the formula is applied to any that is suitable for solving this problem.
DC and AC operation
The magnetic field that is created inside the coil is directed along the axis, and is equal to:
where µ0 is the magnetic permeability of the vacuum, n is the number of turns, and I is the current value.
When the current moves along the solenoid, the coil stores energy, which is equal to the work necessary to establish the current. To calculate the inductance in this case, the formula is used as follows:
where L is the inductance value and E is the storage energy.
EMF of self-induction occurs when the current in the solenoid changes.
In the case of AC operation, an alternating magnetic field appears. The direction of gravity may change, but may remain unchanged. The first case occurs when using a solenoid as an electromagnet. And the second, when the anchor is made of soft magnetic material. An alternating current solenoid has a complex resistance, in which the resistance of the winding and its inductance are included.
The most common application of the first type of solenoids (direct current) is in the role of a translational power electric drive. Strength depends on the structure of the core and body. Examples of use are the operation of scissors when cutting checks in cash registers, valves in engines and hydraulic systems, tongues of locks. The second type solenoids are used as inducers for induction heating in crucible furnaces.
Vibrational contours
The simplest resonant circuit is a series oscillatory circuit consisting of switched on inductors and a capacitor through which alternating current flows. To determine the inductance of a coil, the formula is used as follows:
where XL is the reactance of the coil, and W is the circular frequency.
If capacitor reactance is used , the formula will look like this:
Xc = 1: W x C.
Important characteristics of the oscillatory circuit are the resonant frequency,
wave impedance, and quality factor of the circuit. The first characterizes the frequency where the loop resistance is active. The second shows how the reactance at the resonant frequency passes between such quantities as the capacitance and inductance of the oscillatory circuit. The third characteristic determines the amplitude and width of the
amplitude-frequency characteristics (AFC) of the resonance and shows the size of the energy reserve in the circuit as compared with the energy loss for one oscillation period. In technology, the frequency properties of circuits are estimated using frequency response. In this case, the circuit is considered as a four-terminal. When displaying graphs, the value of the voltage transfer coefficient of the circuit (K) is used. This value shows the ratio of the output voltage to the input. For circuits that do not contain energy sources and various amplifying elements, the coefficient value is not more than unity. It tends to zero when, at frequencies other than resonant, the loop resistance is high. If the resistance value is minimal, then the coefficient is close to unity.
In a parallel oscillatory circuit, two reactive elements with different reactivity are included. The use of this type of circuit implies the knowledge that with the parallel connection of the elements, only their conductivity, and not the resistance, must be added. At the resonant frequency, the total conductivity of the circuit is zero, which indicates an infinitely large resistance to alternating current. For a circuit in which capacitance (C), resistance (R) and inductance are connected in parallel, the formula combining them and quality factor (Q) is as follows:
When the parallel circuit is operating for one period of oscillation, an energy exchange occurs between the capacitor and the coil twice. In this case, a loop current appears, which is significantly greater than the current value in the external circuit.
Condenser operation
The device is a bipolar low conductivity and with a variable or constant value of the capacitance. When the capacitor is not charged, its resistance is close to zero, otherwise it is equal to infinity. If the current source is disconnected from this element, then it becomes this source until it is discharged. The use of a capacitor in electronics is the role of filters that remove interference. This device in power supplies on power circuits is used to power the system at high loads. This is based on the ability of an element to pass an alternating component, but an unstable current. The higher the frequency of the component, the lower the resistance of the capacitor. As a result, through the capacitor, all interference that goes over the direct voltage is suppressed.
The resistance of an element depends on the capacitance. Based on this, it will be more correct to put capacitors with different volumes in order to pick up all kinds of interference. Due to the ability of the device to transmit direct current only during the charge period, it is used as a time-setting element in generators or as a forming pulse element.
Capacitors come in many types. Classification by type of dielectric is mainly used, since this parameter determines the stability of the capacitance, insulation resistance, and so on. The systematization for this value is as follows:
- Capacitors with gaseous dielectric.
- Vacuum
- With liquid dielectric.
- With solid inorganic dielectric.
- With solid organic dielectric.
- Solid state.
- Electrolytic.
There is a classification of capacitors according to their purpose (general or special), according to the nature of protection against external factors (protected and unprotected, insulated and uninsulated, sealed and sealed), according to the installation technique (for mounted, printed, surface, with screw terminals, with snap-on terminals ) Also, devices can be distinguished by the ability to change capacity:
- Constant capacitors, that is, in which the capacitance remains always constant.
- Trimmers Their capacity does not change during the operation of the equipment, but it can be adjusted one-time or periodically.
- Variables These are capacitors that allow the change in its capacity during the operation of the equipment.
Inductance and Capacitor
Current-carrying elements of the device are able to create its own inductance. These are such structural parts as masonry, connecting busbars, down conductors, leads and fuses. You can create additional capacitor inductance by attaching busbars. The mode of operation of the electrical circuit depends on the inductance, capacitance and resistance. The formula for calculating the inductance that occurs when approaching the resonant frequency is as follows:
- Ce = C: (1 - 4Π 2 f 2 LC),
where Ce determines the effective capacitance of the capacitor, C shows the actual capacitance, f is the frequency, L is the inductance.
The value of the inductance should always be taken into account when working with power capacitors. For pulse capacitors, the magnitude of the intrinsic inductance is most important. Their discharge falls on the inductive circuit and has two types - aperiodic and oscillatory.
The inductance in the capacitor is dependent on the connection circuit of the elements in it. For example, when sections and buses are connected in parallel, this value is equal to the sum of the inductances of the main busbar package and the terminals. To find this kind of inductance, the formula is as follows:
where Lk is the inductance of the device, Lp is the package, Lm is the main bus, and Lb is the terminal inductance.
If during a parallel connection the bus current varies along its length, then the equivalent inductance is determined as follows:
- Lk = Lc: n + µ0 l x d: (3b) + Lb,
where l is the length of the tires, b is its width, and d is the distance between the tires.
To reduce the inductance of the device, it is necessary to arrange the current-carrying parts of the capacitor so that their magnetic fields are mutually compensated. In other words, live parts with the same current flow must be removed as far as possible from each other, and closer to each other in the opposite direction. By combining down conductors with decreasing dielectric thickness, the inductance of the section can be reduced. This can be achieved by dividing one section with a large volume into several with a smaller capacity.