Incoming links: Electric current
Unit of electric current.
Affected by the ampere in the 2019 redefinition of the SI base units.
Force between two wires carrying an electric current.
Caused by the Lorentz force.
The fundamental intuition about capacitors is that they never let electrons through.
They can only absorb electrons up to a certain point, but then the pushback becomes too strong, and current stops.
Therefore, they cannot conduct direct current long term.
For alternating current however, things are different, because in alternating current, electrons are just jiggling back and forward a little bit around a center point. So you can send alternating current power across a capacitor.
The key equation that relates Voltage to electric current in the capacitor is:So if a voltage Heavyside step function is applied what happens is:More realistically, one may consider the behavior or the series RC circuit to see what happens without infinities when a capacitor is involved as in the step response of the series RC circuit.
- the capacitor fills up instantly with an infinite current
- the current then stops instantly
Finding capacitance with an oscilloscope by Jacob Watts (2020)
Source. Good experiment.Capacitors Explained by The Engineering Mindset
. Source. 2019.This notation is designed to be relatively easy to write. This is achieved by not drawing ultra complex ASCII art boxes of every component. It would be slightly more readable if we did that, but prioritizing the writer here.
Two wires are only joined if but the following are:
+ is given. E.g. the following two wires are not joined: |
--|--
| |
--+--
|Simple symmetric components:
-,+and|: wireAC: AC source. Parameters:e.g.:Hz: frequencyV: peak voltage
If only one side is given, the other is assumed to be at a groundAC_1Hz_2VG.C: capacitorG: ground. Often used together withDC, e.g.:means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 ADC_10---R_10---GL: inductorMICROPHONE. As a multi-letter symmetric component, you can connect the two wires anywhere, e.g.or:---MICROPHONE---| MICROPHONE |SPEAKERR: resistorSQUID: SQUID deviceX: Josephson junction
Asymmetric components have multiple letters indicating different ports. The capital letter indicates the device, and lower case letters the ports. The wires then go into the ports:
D: diodeSample usage in a circuit:a: anode (where electrons can come in from)c: cathode
Can also be used vertically like aany other circuit:--aDc--We can also change the port order, the device is still the same due to capital| a D c |D:--cDa-- | Dac-- | Dca-- | --caDDCDC source. Ports:E.g. a 10 V source with a 10 Ohm resistor would be:p: positiven: negative
If only one side is given, the other is assumed to be at a the ground+---pDC_10_n---+ | | +----R_10------+G. We can also omitpandmin that case and assume thatpis the one used, e.g. the above would be equivalent to:If the voltage is not given, it is assumed to be a potentiometer.DC_10---R_10---GT: transistor. The ports aresgTd:Sample usage in a circuit:s: sourceg: gated: gate
All the following are also equivalent:---+ | --sgTd--| g --sTd-- | --Tsgd-- |I: electric current source. Ports:s: electron sourced: electron destination
V: Voltmeter. Ports:If we don't need to specify explicit positive and negative sides, we can just use:p: positiven: negative
without any ports. This is notably often the case for AC circuits.---V---Optionaly, we can also add the sides as in:
Numbers characterizing components are put just next to each component with an underscore. When there is only one parameter, standard units are assumed, e.g.:means:Micro is denoted as
+-----+
| |
C_1p R_2k
| |
+-----+- a capacitor with 1 pico Faraday
- a resistor with 2 k Ohms
u.Wires can just freely come in and out of specs of a component, they are then just connected to the component, e.g.:means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 A
DC_10---R_10---GIn 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling".
In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling".
Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:
As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."
It resists to change in electric current. Well seen at: Video "LC circuit by Eugene Khutoryansky (2016)".
The Kibble balance is so precise and reproducible that it was responsible for the 2019 redefinition of the Kilogram.
It relies rely on not one, but three macroscopic quantum mechanical effects:How cool is that! As usual, the advantage of those effects is that they are discrete, and have very fixed values that don't depend either:One downside of using some quantum mechanical effects is that you have to cool everything down to 5K. But that's OK, we've got liquid helium!
- atomic spectra: basis for the caesium standard which produces precise time and frequency
- Josephson effect: basis for the Josephson voltage standard, which produces precise voltage
- quantum Hall effect: basis for the quantum Hall effect, which produces precise electrical resistance
- on the physical dimensions of any apparatus (otherwise fabrication precision would be an issue)
- small variations of temperature, magnetic field and so on
The operating principle is something along:Then, based on all this, you can determine how much the object weights.
- generate a precise frequency with a signal generator, ultimately calibrated by the Caesium standard
- use that precise frequency to generate a precise voltage with a Josephson voltage standard
- convert that precise voltage into a precise electric current by using the quantum Hall effect, which produces a very precise electrical resistance
- use that precise current to generate a precise force on the object your weighing, pushing it against gravity
- then you precisely measure both:
- local gravity with a gravimeter
- the displacement acceleration of the object with a laser setup
How We're Redefining the kg by Veritasium
. Source. The Kibble Balance, realizing the Kilogram from fundamental constants of nature by Richard Green
. Source. Presented in 2022 for a CENAM seminar, the Mexican metrology institute. The speaker is from the Canadian metrology institute- youtu.be/ZfNygYuuVAE?t=854: they don't actually use the Quantum Hall effect device during operation, they only use it to calibrate other non-quantum resistors
The Watt balance and redefining the kilogram by National Physical Laboratory
. Source. Nothing much, but fun to hear Kibble talking about his balance in beautiful English before he passed.In the standard formulation of Maxwell's equations, the electric current is a convient but magic input.
Would it be possible to use Maxwell's equations to solve a system of pointlike particles such as electrons instead?
The following suggest no, or only for certain subcases less general than Maxwell's equations:
This is the type of thing where the probability aspect of quantum mechanics seems it could "help".