Question 1: Define a resistor connected in series and explain how the total resistance is calculated.

Answer: A resistor connected in series is one where resistors are connected end-to-end, so the current flows through each resistor sequentially. The total resistance is the sum of individual resistances: R_total = R1 + R2 + R3 + ...

Question 2: Describe the main difference between resistors in series and resistors in parallel regarding total resistance.

Answer: In series, the total resistance increases and is the sum of individual resistances. In parallel, the total resistance decreases, and the reciprocal of total resistance is the sum of the reciprocals of individual resistances.

Question 3: Explain why adding more resistors in parallel decreases the total resistance of the circuit.

Answer: Adding resistors in parallel provides additional pathways for current, thereby reducing the overall opposition to current flow and decreasing the total resistance.

Question 1: Calculate the total resistance when three resistors of 4 Ω, 6 Ω, and 8 Ω are connected in series.

Answer: R_total = R1 + R2 + R3 = 4 Ω + 6 Ω + 8 Ω = 18 Ω

Question 2: Find the equivalent resistance of two resistors of 12 Ω and 24 Ω connected in parallel.

Answer: 1/R_total = 1/12 + 1/24 = (2/24) + (1/24) = 3/24 = 1/8; R_total = 8 Ω

Question 3: A circuit contains a 9 Ω resistor in series with a parallel combination of two resistors, 3 Ω and 6 Ω. What is the total resistance of the circuit?

Answer: Parallel resistance: 1/R_parallel = 1/3 + 1/6 = (2/6) + (1/6) = 3/6 = 1/2; R_parallel = 2 Ω. Total resistance: R_total = 9 Ω + 2 Ω = 11 Ω

Question 1: Describe a simple experimental setup to measure the total resistance of resistors connected in series. Include the variables you would control and safety precautions you would take.

Answer: An experiment involves connecting resistors in series to a circuit with a voltmeter and ammeter. Variables include resistor values, supply voltage, and connection consistency. Control variables include ensuring resistors are properly connected, and safety precautions involve checking the circuit for faults, ensuring the power supply is within safe limits, and handling resistors carefully to prevent burns or damage.

Question 1: A circuit has three resistors in parallel with resistances of 2 Ω, 4 Ω, and 8 Ω. If the total current supplied is 6 A, what is the approximate current through each resistor? Explain your reasoning.

Answer: Calculate R_total: 1/R_total = 1/2 + 1/4 + 1/8 = (4/8) + (2/8) + (1/8) = 7/8; R_total ≈ 1.14 Ω. Using Ohm's law: V = IR. Voltage across resistors: V = I_total × R_total = 6 A × 1.14 Ω ≈ 6.84 V. Current through each resistor: I = V / R. For 2 Ω resistor: I ≈ 6.84 V / 2 Ω ≈ 3.42 A; for 4 Ω resistor: I ≈ 6.84 V / 4 Ω ≈ 1.71 A; for 8 Ω resistor: I ≈ 6.84 V / 8 Ω ≈ 0.86 A.

Question 1: Explain how understanding resistors in parallel is important in designing household electrical wiring systems.

Answer: Resistors in parallel are analogous to household wiring, where multiple appliances are connected across the same voltage source. Understanding parallel configurations ensures safe and efficient distribution of current, preventing overloads and ensuring all appliances receive adequate voltage.

Question 2: Describe how resistor networks are used in electronic devices to control current flow and voltage levels.

Answer: Resistor networks in electronic devices are used to divide voltage, limit current, and set biasing conditions. Series resistors can increase total resistance, while parallel networks can reduce resistance, allowing precise control of electrical parameters within the circuit.