question_answer

Arrange the order of power dissipated in the given circuits, if the same current enters at point A in all the circuits and resistance of each resistor is R.

A) (ii) > (iii) > (iv) > (i)

B) (iii) > (ii) > (iv) > (i)

C) (iv) > (iii) > (ii) > (i)

D) (i) > (ii) > (iii) > (iv)

Correct Answer: A

Solution :

            Net resistance, \[{{R}_{AB}}=\frac{R}{3}\]             Power dissipated.             \[{{P}_{AB}}={{l}^{2}}{{R}_{AB}}{{l}^{2}}\frac{R}{3}\]             (ii)                         Net resistance, \[{{R}_{AB}}=3R\]             Power dissipated.             \[{{P}_{AB}}={{l}^{2}}{{R}_{AB}}={{l}^{2}}(3R)=3{{l}^{2}}R\]             (iii)                         Net resistance, \[{{R}_{AB}}=\frac{R}{2}+R=\frac{3}{2}R\]             Power dissipated.             \[{{P}_{AB}}={{l}^{2}}{{R}_{AB}}={{l}^{2}}\left( \frac{3}{2}R \right)=\frac{3}{2}{{l}^{2}}R\]             (iv)                          Net resistance \[\frac{1}{{{R}_{AB}}}=\frac{1}{2R}+\frac{1}{R}=\frac{3}{2R}\]             or \[{{R}_{AB}}=\frac{2}{3}R\]             Power dissipated.             \[{{P}_{AB}}={{l}^{2}}{{R}_{AB}}={{l}^{2}}\left( \frac{2}{3}R \right)=\frac{2}{3}{{l}^{2}}R\] Thus, (ii) > (iii) > (iv) > (i)