How Should Voltage Across an Inductor Be Treated in Circuit Analysis?

[cupid.callin]

Homework Statement

suppose there is a inductor connected to a battery and resistor in series ...

i need to find the current in circuit at some time t
i suppose i could use Kirchhoff's loop law but i don't know weather to take potential across inductor (L di/dt) as positive or negative.
i suppose i should use it as negative because it is opposing the emf of battery but i am not sure

but this thing will not work in case of discharging LR circuit ... some help please ... ... ... ...

 

[collinsmark]

Homework Statement

suppose there is a inductor connected to a battery and resistor in series ...

i need to find the current in circuit at some time t
i suppose i could use Kirchhoff's loop law but i don't know weather to take potential across inductor (L di/dt) as positive or negative.
i suppose i should use it as negative because it is opposing the emf of battery but i am not sure

but this thing will not work in case of discharging LR circuit ... some help please ... ... ... ...

You can figure this out.

Suppose there is no initial current. In other words, suppose the circuit is such that at time t = 0, the circuit is closed and i₀ = 0 (at that instant in time).

Now sum the voltages all the way around in a loop. You'll have to calculate the voltage drop across R, but that should be pretty easy since at this instant in time, i = 0. Then note that the sum of all the voltage drops, all the way around the loop should equal zero, per one of Kirchhoff's laws.

So what polarity does the voltage across the inductor have to be to insure that Kirchhoff's law(s) are satisfied?

 

[ehild]

i don't know weather to take potential across inductor (L di/dt) as positive or negative.
i suppose i should use it as negative because it is opposing the emf of battery but i am not sure

The potential refers to a point. Potential difference is "across".
In an inductor, an is emf induced due to changing current. It is -L dI/dt. You can consider it as an additional voltage source that has opposite sign as that of the "real" source.

ehild

 

[cupid.callin]

You can figure this out.

Suppose there is no initial current. In other words, suppose the circuit is such that at time t = 0, the circuit is closed and i₀ = 0 (at that instant in time).

Now sum the voltages all the way around in a loop. You'll have to calculate the voltage drop across R, but that should be pretty easy since at this instant in time, i = 0. Then note that the sum of all the voltage drops, all the way around the loop should equal zero, per one of Kirchhoff's laws.

So what polarity does the voltage across the inductor have to be to insure that Kirchhoff's law(s) are satisfied?

The potential refers to a point. Potential difference is "across".
In an inductor, an is emf induced due to changing current. It is -L dI/dt. You can consider it as an additional voltage source that has opposite sign as that of the "real" source.

ehild

i can do this to find the sign but i need the reason that why is sign like that ...

and sorry for late reply ...

 

[ehild]

It is the consequence of Maxwell's laws. They are the fundamental laws of electrodynamics, based on experimental facts. You cannot ask, why.

ehild

 

[cupid.callin]

why not ... everything in physics has a reason ,,, weather we know it or not

 

[ehild]

Well, you can think that in case the opposite were true, and positive electromotive force were induced by a changing current, the induced emf would rise the current even more in a circuit and the circuit would blow away. If such law existed in the history of the universe in some world, that world would not have been stable and can not exist now.

ehild