The sign in the formula for the voltage across the inductor

This question is about voltage induced in a inductance.

I know the rate of change of current induces EMF in the inductor. The direction of the induced EMF will be opposite to the change that is causing it. The EMF induced is given by the following formula.

$$V_l = -L \frac{dI}{dt}$$

The negative sign indicates direction of induced emf across the coil is opposite the current change.

In the picture I have drawn current direction and \$V_l\$ direction.

If \$\dfrac{dI}{dt}\$ is postive, \$V_l\$ will be negative according to formula right? Or does the direction of \$V_l\$ has to be reversed?

In many Internet references I found \$V_l = L \dfrac{dI}{dt}\$. Which one is correct?

I hope they reversed \$V_l\$ reference points and removed the negative sign in the formula. Please clarify.

Answer

The way you drew it, I and \$\frac{dI}{dt}\$ are both positive in the direction of the arrow and the correct expression is

\$V_L = L\frac{dI}{dt}\$

The negative sign depends on the direction you define your voltage and current.

^{simulate this circuit – Schematic created using CircuitLab}