A) 2 : 4 : 3
B) 8 : 4 : 12
C) 4 : 8 : 27
D) 8 : 4 : 27
Correct Answer: D
Solution :
(d) 8 : 4 : 27 Current through \[2\,\Omega \], resistor \[{{l}_{1}}=\frac{2l}{3}\] Heat produced per second, \[{{H}_{1}}=l_{1}^{2}\times 2={{\left( \frac{2l}{3} \right)}^{2}}\times 2=\frac{8{{l}^{2}}}{9}\] Current through \[4\,\Omega \], resistor \[{{l}_{2}}=\frac{l}{3}\] Heat produced per second \[{{H}_{2}}=l_{2}^{2}\times 4={{\left( \frac{l}{3} \right)}^{2}}\times 4=\frac{4{{l}^{2}}}{9}\] Current through \[3\,\Omega \] resistor \[=l\] Heat produced \[{{H}_{3}}={{l}^{2}}\times 3\] \[=3{{l}^{2}}=\frac{27{{l}^{2}}}{9}\] \[\therefore \,\,{{H}_{1}}:{{H}_{2}}:{{H}_{3}}=8:4:27\]
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