Question 1: Resistors are components used to limit the flow of electric current in a circuit. When resistors are connected in series, the total resistance is the sum of individual resistances. In parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances. Understanding these configurations helps in designing efficient electrical systems.

Answer: Resistors in series add directly; in parallel, reciprocal of total resistance is sum of reciprocals.

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

Answer: Resistors are in series when connected end-to-end in a single path for current.

Question 2: Explain how the total resistance changes when resistors are added in parallel.

Answer: Adding resistors in parallel decreases the total resistance because the reciprocal sum increases.

Question 3: What is the formula for calculating the equivalent resistance of two resistors in parallel?

Answer: 1 / R_eq = 1 / R_1 + 1 / R_2

Question 1: Calculate the total resistance when three resistors of 4 Ω, 6 Ω, and 12 Ω are connected in series.

Answer: R_total = R_1 + R_2 + R_3 = 4 + 6 + 12 = 22 Ω

Question 2: Find the equivalent resistance of two resistors of 8 Ω and 12 Ω connected in parallel.

Answer: 1 / R_eq = 1/8 + 1/12 = (3/24 + 2/24) = 5/24; R_eq = 24/5 = 4.8 Ω

Question 1: Describe a basic experiment to determine whether resistors are in series or parallel in a circuit. Include the variables you would measure and safety precautions.

Answer: Set up a circuit with known resistors and measure the total resistance. Vary the connections and record how the total resistance changes. Variables include resistor values, connection type, and measured resistance. Safety precautions include ensuring the power supply is turned off before modifying connections, using appropriate resistors to prevent overheating, and checking connections for shorts.

Question 1: A circuit contains three resistors: 5 Ω, 10 Ω, and 15 Ω. When connected in series, the total resistance is 30 Ω. When connected in parallel, the total resistance is approximately 2.14 Ω. Explain why these values differ significantly.

Answer: In series, resistances add directly, resulting in higher total resistance. In parallel, the reciprocal sum results in a much lower resistance due to multiple pathways for current.

Question 2: Given data: Resistors of 3 Ω, 6 Ω, and 9 Ω are connected in parallel. The measured total resistance is 1.64 Ω. Confirm this value through calculation.

Answer: 1 / R_eq = 1/3 + 1/6 + 1/9 = (3/9 + 1.5/9 + 1/9) = 5.5/9; R_eq = 9/5.5 ≈ 1.64 Ω

Question 1: Explain how resistors in parallel are used in household wiring or electronic devices to ensure safety and functionality.

Answer: Resistors in parallel allow multiple current pathways, reducing total resistance and preventing overloads. This configuration is used in household wiring to distribute current safely and in electronic devices to regulate voltage and current flow efficiently.

Question 2: Discuss how understanding resistor networks can influence the design of electronic circuits in modern technology such as smartphones or computers.

Answer: Knowledge of resistor networks allows engineers to optimise circuit performance, manage power consumption, and prevent overheating. In smartphones and computers, resistor configurations are crucial for signal processing, voltage regulation, and ensuring device safety and efficiency.