Overview

The purpose of this essay is to convey the fundamentals of electricity and electronic parts.

Ohms Law

First, some definitions are in order, as well as some analogies. Voltage, measure in Volts, is the difference in charge between one point and another in an electrical circuit. In the hydraulic analogy, which is a way of relating non-intuitive concepts in electromagnetism to the more familiar concepts in hydraulics, electric potential is equivalent to the pressure experienced by water flowing through a pipe, and voltage (or voltage drop or potential difference) is equivalent to the different in pressure between two points. This is measured in volts. Electric current is analogous to the volume flow rate. This is measured in Amperes. A unit of electric charge is analogous to a unit volume of water. The wire used for conducting electricty can be thought of as a pipe, with capped ends. When a wire is attached to a circuit, one end is uncapped, and unless the other end is uncapped, you'd expect nothing to occur. A resistor is the equivalent of a constricted pipe, limiting the amount of current through at a given moment. To pass the same amount of water through the pipe at a given moment (the current), you'd need to increase the pressure, the voltage, without going over the pressure limit of the pipe. A node, or junction, where two wires meet, is analogous to a piping tee, and the net flow of water (current) must be equivalent into and out of the junction. A capacitor is equivalent to a water tank, which stores water coming from one pipe before discharding that water into another pipe. If there is an accumulation of water after the first pipe stops, water will continue to flow. Much in the same way, a capacitor works to smooth out interruptions in the current, such that electrical potential can be stored for short periods of time and discharged. Capacitors are measured in both voltage, the maximum voltage a capacitor can handle, as well as capacitance, with units of Farads or microFarads. One farad is equivalent to the ability to store 1 Coulomb of charge when attached to a 1 Volt source, 1 F = C / V. These often used to smooth out peaks when converting from AC to DC power. An inductor is a component in a circuit that stores energy within its electric field, and the energy of the magentic field is then converted into electrical energy. An inductor is analogous to a water wheel. It takes some time to get "up to speed" so as to not cause resistance, but once it's up to speed, water will flow through it, and if there is another route with some resistance, like a light bulb wired in parallel, back to the source, the current will flow through the water wheel at this time. If the current from the source stops, the inductor will continue power the circuit for some time, until the "wheel stops spinning." Inductors are used for things like boost converters to increase DC output voltage, choke AC supply and allow only DC to pass, filter and separate different frequencies, and for transformers, motors, and relays. Inductance is measured in Henry (H) which equals 1 Volt of EMF across the inductor with 1 Ampere of current. The higher the inductance, the more energy it can store within its magnetic field. Power could be thought of as the water used up in a steam engine, it is the rate of electrical energy transferred or consumed. This is measured in watts (W), with one Watt equaling one joule or energy per second. That should be sufficient for now as far as electronic concepts are concerned, now let's discuss the noteworthy relationships within electrical engineering, at the basic level.

Like I said above, the Voltage, or the pressure experienced by the energy in the electromagnetic fields to move in one direction, is proportional to the current, or the energy flow rate, and any resistance experienced along the way. This is known as Ohm's law, V = I * R. The variables of this equation can be manipulated to find the current given the resistance and voltage, as well as the current given the voltage and resistance. Power, the rate of energy usage, is also equivalent to the voltage multiplied by the current. This gives a relationship of P = V * I. From the above explanation (around current being the rate of flow) this might seem unintuitive, as you could imagine that all you would need to determine the amount of energy dissipated as heat to be entirely proportional to the current, or energy flowing into the resistor. This is actually due to my poor explanation, and verbiage around current. Taking a different anaology, think of electrons as delivery trucks that carry energy as the cargo (voltage). Current then is the number of trucks passing a point every second, whereas the voltage is how much cargo each individual truck is carrying. So if you want to know how many boxes are beling delivered to a building (or energy is being delivered to a resistor) you need to understand both the rate at which that energy can be transported, but also the energy being trasported. Knowing the units of both current and voltage might help make this more clear. Voltage is defined as Joules per Coulomb (J/C). It expresses how much energy (Joules) is given to each charge (C). Current, measured in Amps, is defined as Coulombs per Second (C/s). It represents how much charge (C) passes by every second (s). As an aside, a Coulomb is just amount of electric charge transported by a constant current of one Ampere per second. Going back to our equation, P = V * I, let's see what happens to the Coulombs. P = (Joules / Coulomb) x (Coulombs / Seconds) = Joules / Second. This gives ou the amount of energy being transferred per second, which is power. Without voltage, we only have a measure of general "stuff" moving, without any knowledge as the quantity of stuff. Actually a better analogy, that actually gets at the heart of "energy" is to think of a crowd of people (the resistor). Now tell a group of 20 people to go through the crowd. This is the current, how many people are moving through this crowd. If they are sprinting they are carrying a massive amount of energy. This energy is their potential energy, or electric potential energy (qV) created by the "push" from the voltage difference. If someone then runs into someone in the crowd, lots of energy will transfer, and in the case of atoms inside the resistor, heat up. This is why we need both the current (people that are moving through the crowd) and voltage (at what speed they are moving through the crowd). Tying this all together then, voltage is the current times resistance. If you know how many people are moving through the crowd, and how much energy was lost when they started crashig into the crowd, you'll know how much potential energy they had to begin with (v). Also, if the crowd is twice as thick (2R), you'd have to push twice as hard (2V) to keep the same number of people moving through. Power can be calculated by the current and the voltage in the same way. If we know the number of sprinters going into a crowd, and the amount of energy the sprinters had before the crowd (or how hard they're being pushed) then we'll know exactly how much energy is expected to be lost/dissipated in the resistor.
Next, let's talk about resistors. Resistors placed on a circuit in series can have varied resistance, but will have the same magnitude of current flow running through them. Because of this each will have varied voltages across themselves, and each will experience a voltage drop, porportionate to the current and resistance. The main rule is that the sum of voltages across each resistor needs to sum to the batteries voltage. V(battery) = VR1 + VR2 + VR3. Because the current magnitude will be lessened with each additional resistor put on the circuit, you can calculate the current by diving the batteries voltage by the total resistance across the circuit.
However, Parallel circuits work in the complete opposite way. Each current must be calculated indiviudally, in a case where there are multiple resistors in parallel. The equation I1 = V/R1 and I2 = V/R2 allows you to do this. The total of these two currents will sum together where those wires meet, Itotal = I1 + I2, and is the current that flows through the battery. To calculate the resistance of a circuit with resistors in parallel is R(total) = ( 1 / (1/R1) + (1/R2) + (1/Rn) ..). First thing that is done in this equation is to convert resistance into conductance, by taking the reciprocal of the resistance at each resistor (1/Rn), since condutance and resistance are opposite. Because they're all conducting current independently, we can't sum their resistance, but we can sum their conduction, so that is what is done in the denominator. Then we divide one by the sum of the conductance to flip the value back to the total resistance. Some good rules of thumb to start developing an intuition around resistance is that if you're looking at resistors in parallel, the total resistance will always be less than they lowest resistor in the group. If they're all equal, then all you need to do is divide one of the multiple resistors by the number of resistors, i.e. if you have 4 100 Ohm resistors in parallel, the total resistance is 100/4 = 25 ohms. It's important to remember that finding the exact number of ohms is less useful than understanding generally what is going on in a circuit. A voltage divide is a way of creating lower voltage portions of circuit. If you take a couple of resistors in parallel hooked up to a 10V battery, and say one is 250 Ohms and one is 750 OHms, doing the calculations to find the current, you'll end up with a V = I x R = 10V / 1000 Ohms = 0.01 Amperes, or 10 mA. Finding the voltage drops across the 250 Ohm resistor then, V = 0.01 x 250 = 2.5 V. If you need a lower voltage portion of the circuit, using a resistor to lower the voltage by using a voltage drop is one way to achieve this. The next thing to speak about is ground, or GND if you're looking at a schematic. When speaking about voltage readings, we say that they a relative, and the thing they are relative to is the ground, an arbitrarily defined point in the circuit that is a zero voltage reference.

###Sources https://www.youtube.com/@leosbagoftricks3732