Question

'$n$' identical bulbs, each designed to draw a power $P$ from a certain voltage supply are joined in series across the supply. The total power which they will draw is :-

• A. $P$
• B. $nP$
• C. $\frac{P}{n^2}$
• D. $\frac{P}{n}$

Answer 1

The correct option is D $\frac{P}{n}$

Let resistance each bulb $=R$ and voltage of source $=V$

Power of each bulb is $P=V^2/R$ or $R=V^2/P$

As n bulbs are in series so total resistance $R_t=nR$ and current $i=V/R_t=V/nR$

Total power drawn is $P_t=i^2{R}_t=\frac{V^2}{n^2{R}^2}\left(nR\right)=\frac{V^2}{nR}=P/n$