A) \[4:2:3\]
B) \[8:4:27\]
C) \[2:4:3\]
D) \[27:8:4\]
Correct Answer: B
Solution :
: Current in resistance R is \[{{I}_{1}}=\frac{12R}{R+2R}=\frac{2}{3}I\] Heat produced in resistance R in time t is \[{{H}_{1}}=I_{1}^{2}Rt={{\left( \frac{2}{3}I \right)}^{2}}Rt\] Current in resistance 2R is \[{{I}_{2}}=\frac{IR}{2R+R}=\frac{1}{3}I\] Heat produced in resistance 2R in same time t is \[{{H}_{2}}=I_{3}^{2}2RT=\left( \frac{1}{3}I \right)2RT\] Current in resistance 1.5R is \[{{I}_{3}}=I\] Heat produced in resistance 1.5R in same time t is \[{{H}_{3}}=I_{3}^{2}(1.5R)t={{I}^{2}}(1.5R)t\] \[\therefore \]\[{{H}_{1}}:{{H}_{2}}:{{H}_{3}}={{\left( \frac{2}{3}I \right)}^{2}}Rt:{{\left( \frac{1}{3}t \right)}^{2}}2Rt:{{I}^{2}}(1.5R)\] \[=\frac{4}{9}:\frac{2}{9}:\frac{3}{2}=8:4:27\]You need to login to perform this action.
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