Sign conventions for Kirchhoff's loop rule

[Meow12]

Homework Statement

Describe the sign convention for Kirchhoff's loop rule in a battery, capacitor, resistor, and inductor.

Relevant Equations

##\sum V=0##

Battery and Capacitor
For a battery (or capacitor), the potential increases by ##\mathcal{E}## (or ##\displaystyle\frac{q}{C}##) as we move from -ve to +ve terminal (or plate) regardless of the direction of the assumed current.

Resistor and Inductor
Suppose we are traversing the loop in the same direction as the assumed current.
The potential decreases by ##iR## as we travel through the resistor.
The potential decreases by ##\displaystyle L\frac{di}{dt}## as we travel through the inductor.

Is this correct?

(I know that strictly speaking, Kirchhoff's loop rule must be modified before being used in a circuit with an inductor as the electric field is non-conservative. Let's assume that we've made the required modification.)

 

[Delta2]

I think you are right. For the inductor it is a "whole can of worms" this subject though.
https://www.physicsforums.com/threads/inducing-emf-through-a-coil-understanding-flux.940861/
And for the capacitor the + terminal is the one we first meet as we traverse the loop in the direction of the assumed current

 

[Meow12]

And for the capacitor the + terminal is the one we first meet as we traverse the loop in the direction of the assumed current

I did not know that. Could you please explain why?

 

[Delta2]

I did not know that. Could you please explain why?

Because the the direction of current is the direction of flow of positive charges, that they first meet the positive terminal and they gather there and then via the mechanism of electrostatic induction they induce equal and opposite charge on the other terminal.

I was wondering btw how else could you find the positive terminal of capacitor. Some capacitors (the so called electrolytic capacitors) have prescribed polarity like the batteries, did you mean that?

 

[Meow12]

I was wondering btw how else could you find the positive terminal of capacitor. Some capacitors (the so called electrolytic capacitors) have prescribed polarity like the batteries, did you mean that?

No, I didn't mean that. My textbook marks the positive terminal of capacitors in circuits, so I never had to rely on the method you just described. Thanks!

 

[Meow12]

And for the capacitor the + terminal is the one we first meet as we traverse the loop in the direction of the assumed current

I just want to clarify one thing--this is true only when the capacitor is being charged, right? Not when it is being discharged?

When the capacitor is being discharged, I think we first meet the - terminal as we traverse the loop in the direction of the assumed current. Because the positive charges in the wire strive to neutralize the negatively charged terminal.

 

[Delta2]

I just want to clarify one thing--this is true only when the capacitor is being charged, right? Not when it is being discharged?

When the capacitor is being discharged, I think we first meet the - terminal as we traverse the loop in the direction of the assumed current. Because the positive charges in the wire strive to neutralize the negatively charged terminal.

Yes you are correct.

 

[Natha]

In the case that it is being discharged, would you need to let ##I = -\frac{dQ}{dt}##, instead of ##I = \frac{dQ}{dt}##? Also what do you do if you do not know whether it is being charged or discharged? Would assuming the sign always give you the right answer? Would you just get a negative Q in your answer (what would be the indicator that you picked the wrong direction)?