Ohm's law, the practical way

Hi,

I am sure everybody here is very well aware of ohm's law. V=I*R, or R = V/I. It's also well-known that connecting resistors in parallel to a power source means that the same amount of "V" will "fall" on the resistors, and the amount of "I" will be "distributed" depending on the resistor's resistance. Amen.

Now... it took me a while to come to terms with the fact that having resistors in parallel means that the total resistance is less than the resistance imposed by the smallest resistor. This is clear if you do the maths and if you look at the formulas, but it's not as clear in an "intuitive" sort of way: how can more resistors resist... less? (the answer to me came from different angles, but that's a different stories).

Now... how do you normally end up using resistors while making up circuits? What's the most commonly used patterns?

The one I can see from several projects is:

  • You have a 5V power source
  • You connect things in parallel to that power source
  • You make sure whatever you connect gets the right amount of amps within its tolerance using a resistor
  • You make sure you don't connect "too much", as you will eventually run our of amps the battery can actually supply

Is this what "normally" ends up happening?
(I am not saying "always", I am saying "most often than not")

Merc.

  • You make sure whatever you connect gets the right amount of amps within its tolerance using a resistor

Only for certain devices, like LEDs.

Other types of devices draw the current they require. In those cases adding a resistor is almost always a bad idea.

Hi,

Ok. But... In general things get connected in parallel right?

Merc.

Depends what you're trying to achieve, but yes. In essence, your arduino digital outputs are connecting external devices/components, in parallel, to the 5v power source (I.e. the same amount of voltage "falls" across all the outputs.

Don’t mix up the idea of parallel resistors (i.e. both ends of all resistors connected together) with a fan-out of resistors from one point to several different end-points. With the fan-out each resistor is separate and probably unaffected by the others.

ResistorFan.jpg

…R

This is clear if you do the maths and if you look at the formulas, but it's not as clear in an "intuitive" sort of way: how can more resistors resist... less?

The water-flow analogy IS intuitive.* Two thin-restrictive pipes, or two partially-on valves give you two water-flow paths, and more total water-current flows.

You can probably derive all of this from Ohm's Law, but it's [u]Kirchhoff's Laws[/u] that describe how voltages & currents add-up or divide in series and parallel circuits.

Now... how do you normally end up using resistors while making up circuits? What's the most commonly used patterns?

The most common use of resistors in digital circuits is as [u]pull-up resistors[/u]. And frequently, the pull-up resistor is part of a [u]wired-or connection[/u].

In analog circuits, resistors are often used as [u]voltage dividers[/u] to provide a (low current) reference or bias voltage.

Resistors are also used simply to limit/control current in non-linear circuits** with LEDs or with the bass-emitter junction of a transistor.

The one I can see from several projects is:

  • You have a 5V power source

  • You connect things in parallel to that power source

  • You make sure whatever you connect gets the right amount of amps within its tolerance using a resistor

  • You make sure you don't connect "too much", as you will eventually run our of amps the battery can actually supply

Yes... If you have a power supply rated at 1 Amp and you connect a lamp (or something) that takes 1 Amp, that's fine. If you connect a 2nd lamp, the 2nd one will also try get 1 Amp and something unpredictable can happen... The voltage may drop, the power supply may burn-up etc.

The same thing will happen if you plug-in two hair dryers and a toaster to the same power outlet. (They are connected in parallel). You'll draw excessive current and blow a circuit breaker. On the other hand, nothing bad will happen if you plug-in 2 or 3 100W lamps, and a maybe a TV.

  • You make sure whatever you connect gets the right amount of amps within its tolerance using a resistor

NO!!! You'll get a voltage drop across the resistor (Ohm's Law) so you won't have 5V for whatever you're powering. You are making a voltage divider, but the resistance of the load is unknown, and usually not constant. For example, we could measure the current drawn by the Arduino and calculate it's resistance... But if you turn-on an LED (powered by the Arduino) the current will increase, which means the resistance has changed.

  • The water flow analogy is imperfect, especially since an open water pipe allows unrestricted water flow and water spills-out everywhere, whereas an open electrical connection is infinite resistance and no current flows. Also, nothing bad happens with zero water-flow resistance, but bad things can happen with no electrical resistance (a short circuit).

** An LED (like all diodes) is non-linear. That is, the resistance changes (drops) as voltage increases. At the diode's breakdown voltage ("operating voltage" for an LED) resistance suddenly drops to almost zero... A very tiny increase in voltage results in a huge increase in current. If there is no resistor to limit the current, the LED (and sometimes whatever is driving the LED) will burn-up.

Hi,

it's not as clear in an "intuitive" sort of way: how can _more_resistors resist... less?

Resistors are most often used to control current. So it helps if you think about current with resistors.

Parallel resistors provide another path for current to flow. So together they resist current less.

mercmobily:
how can more resistors resist… less?

Not if connected in series.

More resistors in series means less current for a given voltage; implies more resistance.

More resistors in parallel means more current for a given voltage; implies less resistance.

Don’t confuse total number of resistors with total equivalent resistance.

It actually becomes a bit easier when you know about resistance’s reciprocal unit, condunctance. The equation symbol is G, and the unit is siemens. Yes, it is pronounced that way, so take a minute to get the sniggers and chortles out of your system before continuing.

Conductance is the reciprocal of resistance. In other words, R = 1/G, and G = 1/R.

Connecting elements in series increases their total resistance, because there are more obstructions in the way, but adding them in parallel increases conductance.

For series resistances, RT = R1 + R2 + R3 + …

For parallel resistances, GT = G1 + G2 + G3 + …

Ever scratch your head wondering why the formula for parallel resistances is so awful? Why don’t you take the formula I just gave, and replace each G with a 1/R. What do you get? :sunglasses:

This way it’s easy: series increases resistance, parallel increases conductance.

Ah, Conductance, and its bedfellow Admittance. That takes me back to my college days...... :wink:

mercmobily:

  • You make sure whatever you connect gets the right amount of amps within its tolerance using a resistor

DVDdoug:
NO!!! You'll get a voltage drop across the resistor (Ohm's Law) so you won't have 5V for whatever you're powering.

Well, mercmobily is right, when we talk about single, simple components like a LED. A led needs the right amount of amps. Or the right amount of voltage. Same difference in this case! You achieve it by putting a resistor in series with the LED to drop 5 V to some 1.5 V. Or dropping the amps from some toasting 500 mA to 150 mA. Don't quote me on the numbers! A LED works with constant current, which is achieved with a constant voltage. An Arduino needs a constant voltage, but can consume a wide range of current. Therefore Arduino connects directly to a voltage source without any voltage dropping single resistors. A voltage regulator is something different. In itself, it is a voltage source. Hopefully with a constant voltage.

Johan_Ha:
A led needs the right amount of amps. Or the right amount of voltage. Same difference in this case!

Wrong. Not the same difference in the case of LEDs. LEDs are current controlled devices, not voltage controlled. Although I believe you already know how LEDs are controlled, your quoted statement will (IMHO) be confusing for OP.

Johan_Ha:
You achieve it by putting a resistor in series with the LED to drop 5 V to some 1.5 V.

Not really. You only size the resistor based on how much current you want while factoring in the built in voltage. Although that is probably what you meant to say, you messed up on the wording (again - confusing OP).

Johan_Ha:
A LED works with constant current, which is achieved with a constant voltage.

Yes and no. An LED works with current period. It can be varying. But you are right that constant voltage and constant load implies constant current.

For calculating parallel resistance, I like the "imagine a voltage" method. :slight_smile:

mercmobily:
Now... it took me a while to come to terms with the fact that having resistors in parallel means that the total resistance is less than the resistance imposed by the smallest resistor. This is clear if you do the maths and if you look at the formulas, but it's not as clear in an "intuitive" sort of way: how can more resistors resist... less? (the answer to me came from different angles, but that's a different stories).

1 drinking straw or narrow tube.... on bottom of a filled water barrel.... poking through the bottom. Water is allowed to run out. But fortunately, the water (current) is limited by 1 straw (resistor).

Poke 999 extra drinking straws to the bottom of the barrel. The water effectively gushes out.

Overall effective resistance ...... lowered significantly by adding more resistors (in parallel). All straws in parallel.

The ends of the straws (where the water exits) all drains into a well (aka ground).

Consider the resistance of straws/tubes to be due to friction.

The idea is the 'open more pathways' between origin and destination, and the overall rate starts to pick up.

mercmobily:
Now... it took me a while to come to terms with the fact that having resistors in parallel means that the total resistance is less than the resistance imposed by the smallest resistor. This is clear if you do the maths and if you look at the formulas, but it's not as clear in an "intuitive" sort of way: how can more resistors resist... less?

Turn on both bath taps and the bath fills quicker - can't get more intuitive than that... Put taps in series
and they are going to resist more than one tap (poor analogy really as taps are not really linear resistances
to flow, but you get the idea).

More paths in parallel, more flow, put paths in series and flow is less. The liquid flow analogy is quite
good really.