Question 1: Explain what is meant by resistors being connected in series.

Answer: Resistors connected in series are linked end-to-end so that the same current flows through each resistor, and the total resistance is the sum of individual resistances.

Question 2: Describe how resistors are connected in parallel and how it affects the total resistance.

Answer: Resistors in parallel are connected across the same voltage source, with their ends connected together, which reduces the overall resistance because multiple pathways allow current to flow simultaneously.

Question 3: Calculate the equivalent resistance of two resistors, 6 Ω and 12 Ω, connected in series.

Answer: R_eq = R_1 + R_2 = 6 Ω + 12 Ω = 18 Ω

Question 4: Calculate the equivalent resistance of the same resistors (6 Ω and 12 Ω) connected in parallel.

Answer: 1 / R_eq = 1 / 6 Ω + 1 / 12 Ω = (2 + 1) / 12 = 3 / 12; R_eq = 12 Ω / 3 = 4 Ω

Question 5: In an experiment, three resistors of 4 Ω, 6 Ω, and 12 Ω are connected in series. What is their total resistance?

Answer: R_total = 4 Ω + 6 Ω + 12 Ω = 22 Ω

Question 6: If the same resistors (4 Ω, 6 Ω, 12 Ω) are connected in parallel, what is the total resistance?

Answer: 1 / R_total = 1 / 4 + 1 / 6 + 1 / 12 = 0.25 + 0.1667 + 0.0833 = 0.5; R_total = 1 / 0.5 = 2 Ω

Question 7: Identify two variables that affect the total resistance in a parallel circuit.

Answer: Number of resistors connected in parallel and their individual resistances.

Question 8: List two safety precautions to observe when building a resistor circuit in a lab setting.

Answer: Ensure the circuit is powered off before making connections and verify resistor ratings to prevent overheating.

Question 9: A device requires a total resistance of 10 Ω. If you have resistors of 5 Ω and 15 Ω, how can you connect them to achieve this resistance?

Answer: Connect the 5 Ω and 15 Ω resistors in parallel. 1 / R = 1 / 5 + 1 / 15 = 0.2 + 0.0667 = 0.2667; R ≈ 3.75 Ω, which is less than 10 Ω. To get 10 Ω, connect resistors in series or adjust resistor values accordingly.

Question 10: Explain a real-life application where resistors in parallel are used.

Answer: Resistors in parallel are used in household wiring to ensure multiple pathways for current, reducing overall resistance and maintaining consistent voltage across appliances.