[Physics] Isn’t the inductor equation negative


The inductor "resists" change in current. So say you measure the voltage across the inductor from point A to point B – the current is flowing in from A towards B. Now say the current is increasing. The inductor will try to oppose the change by creating a current the opposite direction – from point B to A. To do this it will create a voltage, where point A has a lower voltage than point B in order to "encourage" electrons to flow the opposite way. If this is true though, the voltage measured from point A to B will be negative, so shouldn't the equation be:

$$V_{a \to b} = -L\frac{di}{dt}$$

Best Answer

The sign in the case of an inductor is indeed easy to be uncertain about. I would say this is a good illustration of a more general difficulty with signs in physics. The way to get signs right is sometimes not to worry over one equation or another equation of opposite sign, but rather to be clear in your mind about what happens in a simple example case.

I find it very useful to consider the simple circuit with just a resistor and an inductor in it. The voltage around the circuit is zero, so we get the equation

$IR + L dI/dt = 0$

It is easy to see that the sign is correct in this equation, because then we get

$ dI/dt = - (R/L) I$

for which the solution is exponential decay. If we had the opposite sign we would get exponential growth of the current, which is clearly wrong. But you are free to consider the first equation either in the form I wrote it, or in the form

$IR = - L dI/dt$

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