Physics
Physics
Problem
Three household appliances—a room heater of resistance 50 Ω, a fluorescent lamp of resistance 230 Ω, and a ceiling fan whose motor winding has resistance 180 Ω—are each designed to operate from a 230 V mains supply. (a) If the three appliances are mistakenly connected in series to the mains, calculate the equivalent resistance of the circuit and the current drawn from the supply. Hence find the power dissipated in each appliance. (b) Explain, with numerical values obtained, why the series arrangement is unsuitable for domestic use. (c) Now consider the appliances connected correctly in parallel across the same 230 V mains. Determine (i) the current in each branch, (ii) the total current drawn from the mains, and (iii) the total power consumed. (d) Using the results above, derive a general condition that ensures each appliance receives its rated voltage when several appliances are connected in parallel to a single supply.Intuitive explanation
The key insight is understanding how series vs. parallel circuits distribute voltage and current differently. In series, the same current flows through all devices but voltage divides among them—so each appliance gets only a fraction of the mains voltage and operates far below its design. In parallel, each device sees the full mains voltage independently, allowing them to draw their rated current and power. This problem asks you to calculate both scenarios numerically to see why parallel is essential for safe, effective household wiring.
Intuitive explanation
The key insight is understanding how series vs. parallel circuits distribute voltage and current differently. In series, the same current flows through all devices but voltage divides among them—so each appliance gets only a fraction of the mains voltage and operates far below its design. In parallel, each device sees the full mains voltage independently, allowing them to draw their rated current and power. This problem asks you to calculate both scenarios numerically to see why parallel is essential for safe, effective household wiring.