Understanding Kirchhoff's Loop Rule for Inductors and Resistors

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In summary, the conversation is discussing the application of Kirchhoff's loop rule in a circuit with an inductor and resistor. The question is whether the minus sign in the equation should be on the inductor or resistor term. In the given links and explanations, it is determined that the sign can be determined by the direction of current and understanding of steady-state situations. The conversation also touches on the impact of short-circuiting the battery on the current in the circuit.
  • #1
ehrenfest
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Homework Statement


Read the image. I was always confused about this. Is Kirchhoff's loop rule here:

[tex]-L\frac{dI}{dt}+IR = 0 [/tex]

or

[tex] L\frac{dI}{dt}+IR = 0 [/tex]

. Please explain your answer carefully.

Homework Equations


The Attempt at a Solution

 

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  • #3
Well what they do in the second link is use the given fact that the current is increasing to decide what the sign must be. But the same equation should hold whether the current is increasing or decreasing. How do you decide which of my equations to use without knowing whether the current is increasing or decreasing through the inductor?

BTW, the do we know the current is decreasing here? Why?

I don't mean to be rude, but can you help me with this specific example?
 
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  • #4
please show YOUR attempt to solve this first.

explain YOUR thoughts carefully, then someone might help you.
 
  • #5
say we go clockwise around the smaller loop starting from S and record the voltage changes as we go around. How do we get the sign of the first voltage change?
 
  • #6
The battery establishes an initial potential. When the switch has been set for a long time, it means that it has reached a steady-state situation, i.e. the current is constant, which means di(t)/dt = ?

However there is a current and stored energy in the inductor. There is also a voltage drop across the resistor, and only across the inductor when current is changing.

If the battery is by passed, i.e. short-circuited, what then happens to the current?
 

What is Kirchhoff's loop rule?

Kirchhoff's loop rule, also known as Kirchhoff's voltage law, states that the algebraic sum of all the potential differences around any closed loop in a circuit must equal zero. In other words, the sum of all the voltage drops must equal the sum of all the voltage rises in a closed loop.

What is a Kirchhoff's loop rule problem?

A Kirchhoff's loop rule problem is a type of circuit problem where the voltage drops and rises in a closed loop are given, and the goal is to find the unknown voltage or current in the circuit.

How do you apply Kirchhoff's loop rule to a circuit?

To apply Kirchhoff's loop rule to a circuit, you must first identify all the closed loops in the circuit. Then, starting from any point in the loop, assign a direction for the current flow. As you move around the loop, add up all the voltage drops and rises, making sure to account for the direction of the current. The sum of all these voltages must equal zero.

What are the key assumptions when using Kirchhoff's loop rule?

The key assumptions when using Kirchhoff's loop rule are that the circuit is in a steady state, there are no changing magnetic fields, and there are no non-conservative electric fields. Additionally, Kirchhoff's loop rule assumes that the circuit has no branches or junctions within the closed loop.

What are some common mistakes when solving Kirchhoff's loop rule problems?

Some common mistakes when solving Kirchhoff's loop rule problems include incorrect assignment of current direction, missing or misinterpreting a voltage drop or rise, and not properly accounting for the direction of the current in the calculations. It is also essential to ensure that the circuit is in a steady state and that all the branches and junctions within the closed loop are accounted for.

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