# What should be the sign of the voltage across the inductors while doing circuit analysis?

I am not able to understand what should be the sign of the voltage across an inductor while doing circuit analysis. I know the voltage across an inductor is given by -Ldi/dt, when the rate of change of current is increasing,voltage is negative which means its opposing the direction of current and when rate of change current is decreasing,the voltage is positive which means voltage is along the direction of current. But in every book irrespective of the rate of change of current(increasing/decreasing),they are taking the voltage across the inductor to be positive(i.e. v=+Ldi/dt).I dont understand this.I dont think they have applied the same logic here.So would be very helpful if someone could exactly explain whats going on.

It depends on how you choose the direction of the current through an inductor or the voltage polarity. simulate this circuit – Schematic created using CircuitLab

$$u_L = L\dfrac{i_L}{dt}$$

For above circuit, if the current is increasing, then the voltage is increasing also, since the inductor wants to block any further current rising.

Inverted sign example: simulate this circuit

$$u_L = -L\dfrac{i_L}{dt}$$

• I know this concept. But what if the current is decreasing?what will be the sign of the voltage?And why the voltage is positive always in the book? – Rashank Bhardwaj Oct 11 '18 at 11:25
• @RashankBhardwaj I gave you all four combinations. If the current is decreasing then 1,2) voltage has a negative sign; 3,4) voltage has a positive sign. – Marko Buršič Oct 11 '18 at 11:30
• Can I get a more elaborated answer in this part?How do I take the voltage while solving ciruits if the current increasing/decreasing? – Rashank Bhardwaj Oct 11 '18 at 11:38
• @RashankBhardwaj You just choose the arbitrary polarity and current direction, then you use the related formula. – Marko Buršič Oct 13 '18 at 18:03

$$\L\frac{di}{dt}\$$ always opposes the assumed positive direction of current through the inductor. The sign of the resultant analysis then indicates the actual polarity of the induced emf, so you don't have to worry about whether the current is increasing or decreasing or in which direction it's flowing etc... the maths does it all for you.

The general convention in circuit analysis is that current enters from the positive side of an element and outputs the negative side, so when an inductor is sinking current, the side at which the current is entering is positive, when the inductor is sourcing current the current reverses direction and the voltage that was once positive becomes negative.