Theory of circuit algebra?

Question

Ok, this may seem silly, but I am in engineering physics and I want to know what makes equations like ohm's law where V=IR and I = R/V and R = V/I understandable. What I am wondering goes back to simple multiplication and division, so I want to know WHY Voltage is current times resistance, for example. Does this mean voltage equals current # of resistance times? That is a bad sentence but what I'm referring to is something like 2*3 = 2+2+2 so is this like 2A*3Ohms = 2A + 2A +2A? What is the relationship here?

Answer 1

Ohm's Law, like pretty much any other physical law is based on the mathematical ideas of "directly proportional", "inversely proportional", etc.

Let's look at force first: Force = Mass * Acceleration

Why?

If we want to define a thing like force, we think: "well, this thing that I want to call force seems to depend on mass and also on acceleration."

What is important is that force is "directly proportional" to mass and acceleration. Thus, F = k*M*A . But when defining things, we usually set k = 1 to describe the newly invented units (in this case Newtons).

Ohm's Law defines a new concept, "Voltage", in the following way:

- Voltage depends on amps and resistance.

- Bigger voltage (with fixed resistance) means more electrons going through the wire (or whatever). Thus voltage is directly proportional to amperage (# of electron per second)

-Bigger voltage (with a fixed amperage) means a bigger resistance. Thus, voltage is directly proportional to resistance.

Therefore, we have V = k*I*R . But as before, we define the new units by setting k = 1.

And now we have Ohm's Law: V = I * R.

Notice that pretty much ANY physics formula is defined similarly. ( PV = NrT is defined exactly the same way. ) But there are a few exceptions.

Answer 2

To get the voltage, you multiply the current by the resistance. So if you have 2 amps and 3 ohms, then the voltage is given by 2 * 3 = 6 volts. The reason for this is simply that ohms are defined that way. In the real world, this equation never holds exactly. The Ohms Law enthusiasts would say that the resistance value "drifts" with temperature. But the equation still holds so long as you vary R slightly to match the circumstances.

Ohm's law is a very useful equation because it makes it easy to analyze complicated circuits. But for something like a diode, which passes current one way but not the other, Ohm's law does not apply. A diode is said not to be "Ohmic".

Answer 3

Voltage used to be called "electromotive force", "tension", and "electrical potential (difference)".

Voltage is simply a force - a push or a pull.

What gets pushed and pulled?  Electrons.

Electrons move at the speed of light - or close to it.  

By pushing or pulling harder, you don't speed them up - you liberate more of them from their atomic orbits.

A collection of 6.24 x 10^18 electrons is called a coulomb.

When 1 coulomb passes a particular spot in 1 second, we say a current of 1 ampere is flowing.

If you increase the voltage, you increase the quantity of electrons flowing, thus increasing the current.

These electrons flow in conductive materials. The more conductive, the easier it is to liberate the electrons.

Think of it like a multilane highway or bridge.  Regardless of the fixed speed limit, the more lanes you have, the more cars can cross the bridge.  Fewer lanes is like higher resistance.  More cars is like more current.  More voltage is like rush hour - there's more force or demand for cars to get home from work.  Less voltage is like driving at midnight.

Answer 4

Voltage is defined in terms of electrical potential energy.

Current is actually fundamental in SI but can be though of in terms of the amount of charge passing a certain point per second.

Resistance is DEFINED as the instantaneous ratio of voltage to current.

So, to answer your question, Ohm's Law ( V = IR ) is what it is because R is defined as V / I.