10th Class
Science
Electricity and Circuits
Question Bank
Electricity
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)