# Sign of the terms in a circuit

• I
• Silviu
In summary, the sign of the ##L\frac{dI}{dt}## term in DC circuits is dependent on the perspective taken. It can be seen as the voltage drop across the inductor, with a positive sign indicating an increasing current, or as an EMF acting as a voltage source with a negative sign indicating the same. Ultimately, it is important to understand the underlying principles, such as Faraday's law, to determine the correct sign in a given situation.

#### Silviu

Hello! I am a bit confused about the sign of the ##L\frac{dI}{dt}## term in the circuits (DC circuits). In my book it is defined with a minus, on wikipedia it is defined with a plus and I am not sure which one should I use. I can pick any sign I want and the result will come out right regardless? Won't I risk to get a wrong ODE if I have a different sign for that term? Thank you!

Yes. The correct differential equation is ## \mathcal{E}=L \frac{dI}{dt}+IR +\frac{Q}{C} ##, where ## I=\frac{dQ}{dt} ##. ## \\ ## The inductor can be considered to be a voltage source/EMF with voltage ##\mathcal{E}_{inductor}=-L \frac{dI}{dt} ##, which can be put on the left side of the differential equation. Alternatively, it can be considered an element with a voltage drop of ## L \frac{dI}{dt} ## just like a resistor has a voltage drop of ## IR ##. The voltage drop is positive when the current is increasing.

berkeman
Yes. The correct differential equation is ## \mathcal{E}=L \frac{dI}{dt}+IR +\frac{Q}{C} ##, where ## I=\frac{dQ}{dt} ##.
Thank you! So here ##\epsilon## is the sum of any voltage source in the circuit? Something like ##\epsilon = \sum_i V_i##

Yes. And I get the symbol with \mathcal{E} surrounded by the Latex parameters.## \\ ## And please see the last couple of sentences I added to post 2.

Well the signs you understand best when going back to the first principles the circuit equations derive from. For induction it's of course Faraday's law, and there (as with all things having to do with curls and rotation) the right-hand rule is your friend. Here are some notes from a lecture, I've given to Texan engineering students some time ago. Maybe they are of some use (although in my very bad handwriting ;-():

https://th.physik.uni-frankfurt.de/~hees/physics208/phys208-notes-III.pdf

The part on induction you starts on page 106. The course website with some more material is here:

https://th.physik.uni-frankfurt.de/~hees/physics208.html

## 1. What is the sign of the terms in a circuit?

The sign of the terms in a circuit refers to the direction of the current flow and the polarity of the voltage sources. It can be either positive or negative, depending on the direction of the current flow and the polarity of the voltage sources.

## 2. How do I determine the sign of a term in a circuit?

To determine the sign of a term in a circuit, you need to follow the direction of the current flow and the polarity of the voltage sources. If the current is flowing in the same direction as the voltage source's positive terminal, the term will have a positive sign. If the current is flowing in the opposite direction, the term will have a negative sign.

## 3. Can the sign of a term in a circuit change?

Yes, the sign of a term in a circuit can change if the direction of the current flow or the polarity of the voltage sources changes. For example, if the current flow changes direction, a term with a positive sign may become negative and vice versa.

## 4. Why is the sign of a term important in a circuit?

The sign of a term is important in a circuit because it determines the direction of the current flow and the polarity of the voltage sources. This information is crucial in analyzing and understanding the behavior of the circuit, as well as predicting the values of voltage and current at different points in the circuit.

## 5. How does the sign of a term affect the overall circuit?

The sign of a term can affect the overall circuit by changing the direction and magnitude of the current flow and the voltage values at different points in the circuit. It also determines the behavior and operation of different components in the circuit, such as resistors, capacitors, and inductors.