The minimum number of identical bulbs of rating 4 V ; 6 W , that can work safely with desired bright

Question

The minimum number of identical bulbs of rating 4 V ; 6 W , that can work safely with desired brightness, when connected in series with a 240 V mains supply is\

Professor PC Thomas Classes · Answer

(c):Required current for safe working\ $I=\frac{P}{V}=\frac{6}{4}=1.5 \mathrm{~A}$\ Let $N$ number of bulbs are connected in series in the circuit.\ $I=\frac{240}{NR} \Rightarrow N=\frac{240}{IR}...(i)$\Also, Resistance of each bulb, $R=\frac{V^{2}}{P}=\frac{4 	imes 4}{6}=\frac{16}{6}=\frac{8}{3}$\ $N=\frac{240}{1.5 	imes \frac{8}{3}}=\frac{240}{0.5 	imes 8}=\frac{240}{4}=60$\