1. The problem asks about how to calculate total resistance when resistors are added in parallel and in series circuits. 2. For resistors in series, the total resistance $R_{total}$ is the sum of all individual resistances: $$R_{total} = R_1 + R_2 + R_3 + \dots + R_n$$ This is because the current flows through each resistor one after another, so resistances add directly. 3. For resistors in parallel, the total resistance $R_{total}$ is found using the reciprocal sum formula: $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}$$ This is because the current can split across multiple paths, reducing the overall resistance. 4. Important rule: Adding more resistors in series increases total resistance, while adding more resistors in parallel decreases total resistance. 5. Example: For two resistors $R_1=4$ and $R_2=6$ ohms, - Series: $$R_{total} = 4 + 6 = 10$$ ohms - Parallel: $$\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$$ So, $$R_{total} = \frac{12}{5} = 2.4$$ ohms This shows how total resistance behaves differently in series and parallel circuits.