Why Ohm's Law is NOT V=IR - there's more to it! Resistance must be constant - Parth G Physics

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When asked about Ohm's Law, many of us like to remember the equation that gets used to represent it - V=IR, where V is the potential difference or voltage across a circuit component, I is the current through it, and R is the resistance of that component. However, this is a problem, because the same equation can be used for circuit components that DO NOT follow Ohm's Law! In this video, I'll discuss how that can be the case, and what Ohm's Law ACTUALLY says.

As we shall see, Ohm's Law applies to components through which the current I is directly proportional to the voltage V. And the constant of proportionality is then defined as the resistance of the conductor. This is why we get the equation V=IR. However, many of us always forget that in this equation R MUST BE CONSTANT.

For non-ohmic conductors (components that do not follow Ohm's Law, such as diodes, filament bulbs, transistors, and more), the equation V=IR still applies. Except in this case, the value of R need not be constant. It can change with different values of V or I. This is why it makes no sense to say that Ohm's Law is simply the equation V=IR.

Interestingly, for non-ohmic components we can actually measure two different kinds of resistance. For any given value of V and I, we can find the "static resistance" which is simply given by R = V/I, a rearrangement of our favourite equation. However, we can also calculate the gradient (slope) of the component's I-V graph at any given value of V or I. Using calculus, this is technically dV/dI, and this type of resistance is known as "differential resistance". For non-ohmic conductors, these two values of resistance need not be the same as each other, even for the same values of voltage and current! Therefore, we need to be careful in describing which type of resistance we have calculated.

For ohmic conductors, where the I-V graph is simply a straight line, the two types of resistance are equal to each other. Therefore, we can choose to measure either one and just call it "resistance". This is exactly why, in school, you may have been taught that resistance is defined by the equation R = V/I, but been asked to calculate it from a graph by finding the gradient (slope). This is technically incorrect though, right? Just because static resistance and differential resistance are the same for ohmic conductors, does not mean they are the same for non-ohmic conductors! This brings about a misconception that could easily be avoided, by simply asking us to find a point on our I-V graph, and just calculating V/I for that point.

So to summarise, Ohm's Law has a very important condition that we often tend to miss, which is that the resistance of an ohmic component MUST BE CONSTANT. Otherwise, the component is non-ohmic, and the resistance may change, but V=IR still applies.

0:00 - Hey there!
0:30 - A simple anecdote with Pythagoras' Theorem
1:30 - The relationship between voltage, current, and resistance
1:47 - What Ohm's Law ACTUALLY says..
.2:17 - Ohmic circuit components (such as resistors)
2:42 - Non-ohmic conductors (such as diodes, filament bulbs, transistors, and more)
3:12 - Why V=IR still applies for non-ohmic conductors
3:48 - Big thanks to Skillshare for sponsoring this video, check out their free trial linked below!
4:48 - Static Resistance vs Differential Resistance (not the same for non-ohmic conductors)
6:28 - why we find the gradient (slope) of an I-V graph for ohmic conductors, and why this is wrong
7:10 - The big takeaway: V=IR is only Ohm's Law IF RESISTANCE IS CONSTANT!

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Видео Why Ohm's Law is NOT V=IR - there's more to it! Resistance must be constant - Parth G Physics канала Parth G