Simplifying Electrical Circuits: Series and Parallel Resistors
📌 Basic electrical circuits consist of a power source (battery) and components called resistors which control the current flow.
📌 Resistors can be arranged in two primary configurations: series (connected end-to-end like train cars) or parallel (connected side-by-side or across each other).
📌 The goal is to simplify complex mixed circuits (series and parallel combinations) into a single equivalent resistor for easier analysis.

Calculating Total Resistance
📌 For a series circuit, the total resistance ($R_{\text{total}}$) is simply the sum of all individual resistances: $R_{\text{total}} = R_1 + R_2 + ...$
📌 For a parallel circuit, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances: $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$
📌 Example calculation: Two $4\,\Omega$ resistors in parallel result in $R_{\text{total}} = 2\,\Omega$. This is then added to a series component (e.g., $6\,\Omega$) to find the final total resistance ($8\,\Omega$).

Applying Ohm's Law and Analyzing Components
📌 Ohm's Law relates voltage ($V$), current ($I$), and resistance ($R$): $I = \frac{V}{R}$. If $V=20\,\text{V}$ and $R_{\text{total}}=10\,\Omega$, the total current $I = 2\,\text{A}$.
📌 In a series circuit, the current is the same through all resistors, but the voltage divides: $V_n = I \times R_n$. For the example above ($I=2\,\text{A}$), the voltages across $6\,\Omega$ and $4\,\Omega$ resistors are $12\,\text{V}$ and $8\,\text{V}$ respectively.
📌 In a parallel circuit, the voltage across all parallel branches is the same, but the current divides based on resistance: $I_n = \frac{V}{R_n}$. The sum of branch currents must equal the total incoming current (Kirchhoff's Current Law).

Key Points & Insights
➡️ Identify the structure (series or parallel) within a mixed circuit; simplification must start with the parallel sections first when calculating equivalent resistance.
➡️ The total current calculated using $R_{\text{total}}$ must equal the sum of currents in all parallel branches, validating the calculation based on Kirchhoff's Laws.
➡️ To find voltage across individual components in a series connection, use the total circuit current ($I$) multiplied by that component's resistance ($R_n$): $V_n = I \times R_n$.
➡️ To find current through individual components in a parallel connection, use the shared voltage ($V$) divided by that component's resistance ($R_n$): $I_n = V / R_n$.

📸 Video summarized with SummaryTube.com on Nov 28, 2025, 03:15 UTC