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.