| Electronics > Beginners |
| Learning Electronics |
| (1/4) > >> |
| PixieDust:
Hi, I started reading about electronics and I'm a bit stumped pretty much right at the beginning. I don't understand the maths. I'm looking at the current vs time graph. There's obviously two types, DC and AC, both of which intuitively I understand. It's the flow of electrons. DC - electrons flow in one direction, AC - electrons flow in one direction, then in the other. Why however is the current equation i=dq/dt? The current graph is clearly current vs time. Where is q (charge) from? Take direct current. i = 1, so at all points in time, current is 1A. I don't understand how 1 is equivalent to saying i = dq/dt? |
| Moriambar:
--- Quote from: PixieDust on April 30, 2019, 09:28:34 am ---Hi, I started reading about electronics and I'm a bit stumped pretty much right at the beginning. I don't understand the maths. I'm looking at the current vs time graph. There's obviously two types, DC and AC, both of which intuitively I understand. It's the flow of electrons. DC - electrons flow in one direction, AC - electrons flow in one direction, then in the other. Why however is the current equation i=dq/dt? The current graph is clearly current vs time. Where is q (charge) from? Take direct current. i = 1, so at all points in time, current is 1A. I don't understand how 1 is equivalent to saying i = dq/dt? --- End quote --- Hi. The current is defined as the flow of charge in the unit time. You got mixed up on the definitions. DC and AC describe a different Voltage behavior. In order for current to flow you have to have a voltage difference between two points. One of them usually is taken as a reference of being 0V, any other one can be above or below (or equal). Voltage kinda matters only in differences. DC means that the voltages are constant, while AC voltage changes with time. A voltage difference makes a current flow, ie makes charges move, ie makes dq/dt different from 0. Finally the current in many common materials has a proportionality relation with the voltage, ie I=V/R where R is defined as "Resistance". So basically i is CONSTANT in a DC circuit WITH TIME, while in AC it varies |
| pwlps:
Current is defined as the charge flow across the conductor cross section at the point you measure it. So dq/dt stands for the amount of charge crossing the wire cross section at this point per unit time. If you want to see dq/dt as a derivative of a function q(t) you might think of a discharging capacitor, then q(t) will be the charge stored in it. Or of a battery-powered circuit, then q(t) will be the remaining battery charge. |
| Old Printer:
I started this journey a few years ago after tinkering with electronics related gear most of my life, just not understanding how or why much of it worked. Since then I have spent hundreds of hours watching YouTube videos, reading forums and buying/downloading the odd book. YouTube is a great resource for learning, but I found myself wandering from subject to subject, component to component, and ultimately wasting a lot of time. If you are serious about learning electronics as a hobby I would recommend a book like The Art of Electronics and start at page one and work your way through. By jumping around you will be frustrated at trying to learn things that depend on a certain basic level of knowledge you will not have learned yet. You need to master the basic theory and laws, like OHM & Kirchhoff, and work your way through the passive components first. At 66 and being math impaired I have given up on trying to learn all of the math, and instead I have tried to organize calculators for the different equations. It's like building your own library of information and tools and learning to use it efficiently. I simply don't have the years or the need to memorize all that stuff for a hobby, but your situation may be different. All that said, YouTube is a tremendous learning resource if used with some organization. |
| rstofer:
dq/dt is the instantaneous flow of charge past a point. dt is the time interval over which the charge is counted and is made arbitrarily small. In fact dt approaches 0 in a mathematical sense. The reason for taking small slices (samples) of q is that the function is really i(t) = dq/dt. The current i is varying with time and we don't want to miss oddities by having too wide a sample. This example may not help but consider charging a capacitor through a resistor from a battery. Beginning with no charge on the capacitor, once we close a switch and charge (current) begins to flow, the voltage on the capacitor will increase. Here's the point: The dq/dt value changes with the difference in voltage across the resistor - in other words, the difference between the battery voltage and the instantaneous voltage on the capacitor causes a current flow through the resistor and the resistor limits the current. If I use a small resistor, I get a high charge current. This is an important concept and there is a lot to learn from the charge and discharge equations. If you make the time constant (R*C) long enough, say several seconds, you can actually watch the capacitor voltage on a DMM. To be fair, it is easier to see on an analog meter. You will see a large change in voltage early in the charge cycle when the capacitor isn't holding any charge and you will see a very small change when the capacitor voltage is nearly equal to the battery voltage. The small change in charge is exactly the same as saying the current is small since current is defined in terms of charge flowing past a point. Attached is a graph of the charge and discharge of a capacitor scaled to 1V. You can multiply the values by any battery voltage you want. The time constant T (called tau) is 0.1 seconds. You will note that the capacitor charges to 63% of the battery voltage in the first T seconds. Funny thing, it charges to 63% of the difference between battery voltage and capacitor voltage in EVERY T interval. In the second interval, there is 37% voltage difference so we move .63 * 37 or 23%. Now, at the end of 2T seconds, we are at 63 + 23 or 86%.In the 3rd interval, we move up 63% of the remaining 14%. By 6 T intervals, we are essentially at 100% but, mathematically, we never get to 100%. We just get close enough for engineers. The graph is based on 1000 ufd and 100 Ohms, Tau = R * C = 0.1 seconds. Here is a table of Tau versus %Percent Charge: Tau = 0 Percent Charge = 0 Tau = 1 Percent Charge = 63 Tau = 2 Percent Charge = 86 Tau = 3 Percent Charge = 95 Tau = 4 Percent Charge = 98 Tau = 5 Percent Charge = 99 Tau = 6 Percent Charge = 100 The equations Vchg = V0 * (1 - e(-t/Tau)); Vdis = V0 * (e(-t/Tau)); V0 is the battery voltage, Tau = R * C as above If you want to try these on a calculator, just let -t/Tau be neat numbers like -1..-6 Yes, I know this is a bit off the wall but just about everything you need to know about charge on a capacitor and the rate of change of charge (dq/dt) is covered in this example. You can Google for 'capacitor charge' and get far better explanations. If this is too far afield right now, just copy it off and save it for another time. |
| Navigation |
| Message Index |
| Next page |