Question

Three identical resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 27 W. How many times the power would be dissipated if the three resistors were connected in parallel across the same potential difference?

Answer 1

Given:

Power in series combination $P_s=27W$

When they are in series : $R_{eq}=R+R+R=3R,$

and $P_S=\frac{V^2}{R_{eq}}=\frac{V^2}{3R}=27W$
$P_s=3\times 27RW$

When they are in parallel: $R_{eq}=(1/R+1/R+1/R{)}^{-1}=R/3$

Power dissipation , $P_P=\frac{V^2}{R/3}=3\times 3P_S=9\times \left(27W\right)=243W$