I’m not sure if I already know the answer, but sometimes I keep wondering how electrons are involved in this. Maybe I forgot.
If you don’t know the difference between potential (volts) and current (ampers) you can amuse yourself by thinking of dim-witted police catching thiefs with taser guns. Instead of using high voltage these fellows use high amperage. First they need a huge reel of cable and a harpoon to shoot. And if the unlucky thief doesn’t die from the shot he would catch fire because of the amperage.
So high current needs more copper than voltage, because more electrons are passing through. Higher voltage turns dc motors faster than lower voltage. If there are not more electrons envolved, are higher voltage electrons somehow faster?
They may be in a vacuum like in a CRT, but in a conductor, I think that any possible increase in speed would be cancelled out by friction.
Amperage is what you get when you divide Volts by Ohms. Anything else is just an analogy that’s used to illustrate the phenomena.
I’m not sure what you are getting at with your description of a TASER.
A TASER actually works at a rather high voltage and very low amperage, typically 50,000 volts or so but a current of only a couple of milliamps. Most safety standards are built around the idea that currents less than 20 mA are safe and won’t screw up your heart’s rhythm, so the TASER is current limited to keep its max current well below 20 mA. The high voltage is necessary to punch through the skin’s touch resistance as well as clothing that may further insulate the person being tased.
A TASER is designed not to kill (the current is too low) and the amount of power generated is far too low to catch anything on fire.
Higher currents need more copper because current flowing through copper causes heat. The amount of heat that you get is the current squared multiplied by the electrical resistance of the copper (i2R). Try to pass higher currents through too thin of a wire and the wire just melts. Power is the voltage multiplied by the current. One trick that power systems use to keep the i2R losses to a minimum is to use a very simple electrical transformer (basically just two coils of wire around an iron core, often surrounded by oil for cooling and electrical insulation) to increase the voltage. For a given amount of power, if you make the voltage 10 times higher that results in the current being 10 times smaller. That keeps your i2R losses to a minimum and then you just use another transformer at the other end of the wire to drop the voltage back down to something usable.
From an electron point of view, amperes (amps) are a measure of how many electrons are flowing per second through the circuit. 1 amp is 6.242 × 1018 electrons per second. Voltage is a measure of the force pushing those electrons. I suppose you could think of it as the current is how many electrons you have and the voltage is how fast they are being pushed.
Voltage and current are typically inter-related. In other words, in a typical circuit, if you change the voltage then the current also changes. An electrical heating element like the nichrome wire in your toaster is pretty close to an ideal resistor, which has a simple linear relationship between voltage and current, given as V=IR. V is the voltage, I is the current (from the French “intensitie”), and R is the resistance of the wire. Double the voltage and you also double the current. The heat generated in the nichrome wire (which cooks your toast) is the current squared multiplied by the resistance.
Human bodies are not simple resistors. The typical electrical model for a human body is a resistor in series with a resistor and capacitor in parallel, but the values of those components changes with the applied voltage. It’s very tricky to model a human body electrically. V=IR doesn’t work.
That’s only true for linear devices, where the voltage and current are proportional to each other.
Nitpick: amps are a measure of how much charge is flowing per second through the circuit.
The charges may or may not be made up of electrons.
Although it runs into the risk of confusion about the speed of the current I think the hydraulic analogy is helpful here. (As with all attempts at teaching through analogies, there’s a risk I find it helpful because I already understand enough to disregard the differences.)
Voltage is like water pressure, Resistance is like the dimension of the tube, and Current is the flow rate. If you increase pressure/voltage you get higher flow/current. For water this can be increased speed of the water, for electric current in a wire it means more electrons.
Is there a case where instantaneous current and voltage are not proportional to each other?
Sure. In an inductor, any constant current produces no voltage, but a changing current produces a voltage proportional to the rate of change of the current
This is only true for “ohmic” devices (I know, big surprise on the name). Ohmic devices follow Ohm’s law (V=IR, or I=V/R to match the way that you stated it, same thing). Non-ohmic devices do not.
A hunk of metal is ohmic. Most resistors are ohmic, although this may be limited to certain frequencies (wire-wound resistors are non-ohmic at high frequency due to their inductance). Non-ohmic resistors do exist. Semiconductors are usually non-ohmic. Inductors and capacitors are non-ohmic. Any device with hysteresis is non-ohmic (common in electro-magnetic components).
The human body is non-ohmic.
Reactance behaves according to Ohms law. The equivalent circuit for a semiconductor device contains a resistor. The on resistance of an MOS driver is speced in Ohms.
A non-Ohmic device would be magic.
Diodes definitely don’t follow Ohms law. That’s why they’re usually used with a current limiting resistor. Also see ideal voltage & current sources - which, okay, ideal sorta means magic.
The hydraulic analogy of water pressure makes sense. Water droplet is falling faster if it is higher in the first place or goes through valves. But can electrons flow at different speeds? Or is it the frequency of photons (LOL)?
Ohms law: v=iR
Reactance: v = L di/dt, i = C dv/dt
You can use Ohm’s law (sort of) in power systems when you are working with fixed frequencies, in certain limited applications, but inductors and capacitors are very certainly not ohmic.
Your theories about electricity are not consistent with how the rest of the world describes Ohm’s law and things that are ohmic and non-ohmic.
For example, you are going to have an extremely difficult time explaining the step response of a typical RC timing circuit using only Ohm’s law.
This textbook accurately describes Ohm’s law as an empirical rule of thumb that works reasonably well for some substances, yet has many exceptions
OK, I think I’ll escape from this rabbit hole.
Ohm’s law has the most utility when the resistance or impedance of a device is constant or nearly constant.
True if you’re talking about absolute resistance. Not true if you’re talking about slope resistance.
There are actually two kinds of resistances:
- Absolute Resistance.
This is defined as the absolute voltage across the device divided by the absolute current through the device (R=V/I). When people talk about “resistance,” this is usually what they’re talking about; they usually leave off the “absolute” part. For many things, the absolute resistance is more-or-less constant for the device, regardless of the absolute current through it (or equivalently, the absolute voltage across it). This attribute can be handy in electronic circuits. In fact, some devices are specifically manufactured so that the absolute resistance is very “flat” (constant) for the device when it’s used within certain parameters. We call them resistors. They’re cheap and readily available from places like Mouser and Digi-Key. And then there are things that behave like a resistor as a first-order approximation, even though they weren’t specifically designed to be a resistor. One example is a copper wire.
But what if we have a device where the absolute resistance is not constant, and varies a lot depending on the absolute current through it (or equivalently, the absolute voltage across it)? For these devices, it doesn’t make a whole lot of sense to talk about its absolute resistance. As mentioned by @Chopstick, one example is a diode. It would be rather meaningless to say, “With a forward bias current of 1 mA, the diode has a voltage of 0.700 V. Therefore it has a resistance of 700 Ω.” An EE or EE tech will look at you funny if you were to say this. Why? Because if you were to source 2 mA through the diode instead of 1 mA, the voltage across it would be 0.736 V and thus the absolute resistance would be 368 Ω. In other words, by simply changing the current through the diode from 1 mA to 2 mA, its absolute resistance was roughly cut in half! By contrast, the resistance value of a resistor would not change at all if its current were changed by that amount. So as you can see, an absolute resistance calculation for something like a diode is rather meaningless.
- Slope Resistance.
This is also called dynamic resistance, incremental resistance, and small-signal resistance. It is defined as the slope of the voltage vs. current curve for the device at a given point on the curve. It is usually written as dV/dI or ΔV/ΔI. We usually don’t talk about slope resistance for a resistor, or for things that act like resistors, since it’s pretty much the same as its absolute resistance. It is normally used for devices where the absolute resistance is not constant, and varies a lot depending on the current through it (or equivalently, the voltage across it). As mentioned above, one example is a diode. It is perfectly acceptable to say, for example, “With a forward bias current of 1 mA, the slope resistance for the diode is 51 Ω.” Another example would be an incandescent light bulb. (Though strictly speaking, its resistance is a function of temperature, not voltage. But under normal conditions, the temperature of the filament is a function of the power it is dissipating, and thus is a function of IV.)
Lastly, diode curves are usually shown as current vs. voltage, not voltage vs. current. So for curves that show current vs. voltage, the slope resistance is simply the reciprocal of the slope at a point on the curve.
As electrons travel though a conductor they are impeded in their progress by the structure of the metal. They rattle around in the structure an energy is lost to the conductor which (as usual) end up as heat in the material. A large diameter conductor provides more passageway for the moving electrons, so they flow more freely and less energy is lost. The more electrons flowing, or the stronger the push that is moving the electrons along, the more energy there is to be lost into the conductor. Also, the less messy the structure of the conductor the less it impedes the progress of the electrons.
Current is a measure of the flow of charge, usually, but not exclusively electrons. A given number of electrons passing a point in a given time period is the measure of current. The unit of charge is the Coulomb, which is the charge on 6.242 × 10^{18} electrons. One Coulomb per second is one Ampere.
The force pushing the electrons along is the electrical potential, measured in Volts.
In a circuit, the potential force on the electrons moves them around, with a rate governed by the resistance of the circuit. In a simple resistive circuit, the amount the circuit elements impede the progress of the electrons is measured in Ohms. If you have one Volt of potential across a circuit element, and you measure one Amp of current through it, the circuit element exhibits a resistance of one Ohm.
In the resistive element, the potential force is doing work pushing the charge past the resistance. (That work is what turns into heat.) We define the amount of work done in Watts. One Volt pushing one Amp through a resistance does one Watt of work.
The circuit element does not need to be a simple resistor. Jumping ahead, an electric motor also turns electrical potential into work as current flows. Most motors we are familiar with are electro-magnetic in nature (but they need not be). Through the magic of electromagnetics, a motor can look just like a resistor, but it transforms mechanical resistance into electrical resistance (and interestingly vice versa). A motor doing work also transforms electrical potential and current flow into work, and the same deal applies. One Amp at one Volt gets you one Watt of work. (Assuming a perfect motor with no losses.) Or more easily, one thousand Watts is about 1.3 horsepower.
A motor can be designed to run (within engineering constraints) from any voltage. You just need to design the magnetics and conductors to cope with the voltage and losses. Too high a voltage and such mundane issues as failure of wire insulation can occur. Too high a current and the losses mount up. Real life motors have losses in the coils from electrical resistance (see above) and from losses as the magnetic field changes inside the steel of the magnets. Colloquially these are known as copper and iron losses.
Clearly if you increase the voltage applied to any given motor, and there are no restrictions on the current that can be delivered, more force is available to do work and be transformed to motive power. But the ability to deliver current is never actually unlimited. So more voltage does not always translate to running a motor faster.
The speed of electrons in a conductor does vary. But they move remarkably slowly. This is called the drift velocity. There is however no such thing as a higher voltage electron. Electrons move in response to an applied electrical field. The one measured in Volts. More Volts, stronger field. Electrons get pushed harder. The number of electrons moving past a given point is determined by the resistance of a material. But the drift velocity of the actual electrons can vary. If you make a one Ohm resistor from different materials, you will get different drift velocities despite having the same voltage and current. The speed the electrons are moving at in any given conductor is proportional to the voltage. This speed has nothing to do with the speed of light.
When designing any real system everything has resistance. Normal wires have resistance. For a given conductor, if we know its resistance, and the current flowing though it, we also know what voltage there is across the ends of the conductor. So we know the power being dissipated in the conductor. Thus in general use, we look at the current in a conductor, and determine the power being dissipated. This is usually because we have a good idea about the current because of the characteristics of the rest of the system. Not because current by itself determines the power dissipated. We could work it out directly from the voltage drop, but that is a lot messier in general practice.
Since we have formulae for both Ohms law and power, we can combine them.
V = IR
W = IV
so
W = V^2/R = I^2R
The last formula tells us something very useful. It says that for a given conductor, the best way to minimise power losses in the conductor is to use high voltages and thus low current. Which is why we use very high voltages to move power around the countryside.
Here’s my from-the-ground-up primer on parameters used to describe very basic properties of electrical systems, copied from an earlier post:
Electrical charge is measured in coulombs. an electron carries an electrical charge of 1.06x10-19 coulombs.
Current (the flow of electrical charge in a conductor) is measured in amperes (amps). One amp equals one coulomb of electrical charge flowing past your measurement point every second.
In many cases (household appliances, power lines, etc.) the carrier of electrical charge is the electron; based on how much charge an electron carries (see previous paragraph), one amp of current can be expressed as 6.24x1018 electrons flowing past your measurement point every second.
Voltage describes the amount of energy, measured in joules, carried by a unit of electrical charge. Voltage is measured in units of joules per coulomb. So if an electrical current experiences a drop of 1 volt when it flows through an electrical component, then every coulomb of charge that passes by delivers 1 joule of energy to that electrical component. If an electrical current experiences a rise of 1 volt when it flows through an electrical component (e.g. a battery), then every coulomb of charge that passes by receives 1 joule of energy from that electrical component.
Power is energy delivered per unit of time. For electrical devices, the usual unit of power is watts, which is joules per second. (For mechanical devices like motors, they are sometimes rated in horsepower. One horsepower is about 746 watts, i.e. 746 joules per second.)
So if you want to calculate power, you multiply current with voltage:
P = I * V
Using the units for each of those things, you can see why the units cancel out and leave you with the above tidy equation:
Power (joules/second) = current (coulombs/second) * volts (joules per coulomb)
Power (joules/second) = current (coulombs/electron * electrons/second) * (joules per coulomb)
DC electrical motors take electrical power and turn it into mechanical power, but you can also do the reverse: if you apply mechanical power to the shaft, you can extract electrical power from its terminals.
The windings in the motor will produce voltage when you turn the rotor (called back electromotive force, or back-EMF), and that can drive electrical current. The interesting thing is that the DC motor will produce this back-EMF any time it’s turning, even if it’s turning because you’re applying an external voltage to cause it to turn. It offsets the external voltage you’re applying, resulting in less current flowing through the motor. If it spins fast enough, the back-EMF equals your applied voltage, and the current flowing through the motor goes to zero, and you end up with zero torque being developed by the motor. If you want to spin the motor faster, you need to apply a higher voltage; the motor will then speed up a bit more, causing the back-EMF to rise further, once again offsetting your applied voltage and settling in at a particular (albeit higher) speed.
Correct. Or put another way, “Insulation is much cheaper and much lighter than metal,” with the metal usually being aluminum.