> [!summary] Resistors are a component in circuits that reduce the flow of current. > **Key equations:** > Resistors in series: $R_T = R_1 + R_2$ > Resistors in parallel: $\frac{1}{R_{T}}=\frac{1}{R_1}+\frac{1}{R_2}$ >[!info]+ Read Time **⏱ 2 mins** # Definition Resistors are a type of object used in [[Circuits|circuits]]. They reduce the flow of [[Current|current]]. Current gets reduced because of the [[Insulators|insulating]] material that resistors are made of. It's common to call reducing the flow of electrons [[Resistance|resistance]] because of this. Resistors reduce the flow of electrons by converting the energy of electron collisions into heat. # Resistors In Series ![[res_1.png]] [^1] For resistors in series, the current through each resistor is the same. Since they share the same wire. This means that our total [[Potential Difference|potential difference]] of the circuit will be the potential difference of each resistor. >[!warning] Assumption Recall from [[Ohm's Law|ohm law]] that $V = IR$ $\begin{array}{c} V_{T} = V_{1}+V_{2} + V_{3}\\ \cancel{I}R_T = \cancel{I}R_1 + \cancel{I}R_2 \\ R_T = R_1 + R_2 \end{array}$ # Parallel Resistors ![[res_2.png]] [^2] For resistors in parallel the [[Potential Difference|potential difference]] for each resistor is the same. Meaning that our total current is the sum of the junctions by [[Kirchhoff's Laws]]. >[!warning] Assumption Recall from [[Ohm's Law|ohm law]] that $V = IR$ $ \begin{array}{c} I_T = I_1 + I_2 \\ \frac{\cancel{V}}{R_T} = \frac{\cancel{V}}{R_2} + \frac{\cancel{V}}{R_2} \\ \frac{1}{R_{T}}=\frac{1}{R_1}+\frac{1}{R_2} \end{array} $ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/yF7ADcRt_uA?si=xuuFL34LA-vKHOfU" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! --- [^1]: Taken from https://tikz.net/electric_circuit_resistor/ by Izaak Neutelings (Februari, 2020) [^2]: Adapted from https://tikz.net/electric_circuit_resistor/ by Izaak Neutelings (Februari, 2020)