question_answer

Three equal resistors are connected as shown in the figure. The maximum power consumed by each resistor is 18 W. Then maximum power consumed by the combination is :

A) 36 W                                     

B) 18 W

C) 27 W                                     

D) 54 W

Correct Answer: C

Solution :

Key Idea: When resistors are connected in parallel potential difference across them is same. In this circuit combination two resistors are connected in parallel, hence \[\frac{1}{R'}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}\] \[\Rightarrow \]               \[R'=\frac{R}{2}\] Now, these two resistors \[\left( \frac{R}{2}and\,R \right)\]are in  series, hence equivalent resistance is \[{{R}^{'\,'}}=\frac{R}{2}+R=\frac{3R}{2}\] Power across single resistor is 18 W i.e.,  \[p={{i}^{2}}R=18\]        ?(i) Power across combination obtained is \[P'={{i}^{2}}.\frac{3R}{2}\]            ?(ii) Dividing Eq. (i) by Eq. (ii), we get \[\frac{{{i}^{2}}R}{{{i}^{2}}\frac{3R}{2}}=\frac{18}{P'}\] \[\Rightarrow \] \[P'=\frac{3}{2}\times 18=27\,W\]