A) 4 kcal
B) 2 kcal
C) 5 kcal
D) 3 kcal
Correct Answer: B
Solution :
Heat produced in \[5\,\Omega =10\,kcal\] Now from the relation \[{{H}_{1}}=i_{1}^{2}{{R}_{1}}t\] or \[i_{1}^{2}=\frac{{{H}_{1}}}{{{R}_{1}}t}\] or \[i_{1}^{2}=\frac{{{H}_{1}}}{5t}\] ?(1) Again, \[5\times {{i}_{1}}=10\times {{i}_{2}}\] or \[{{i}_{2}}=\frac{{{i}_{1}}}{2}\] Now heat produced in\[4\,\Omega \]resistance is \[{{H}_{2}}=i_{2}^{2}{{R}_{2}}t\] \[i_{2}^{2}=\frac{{{H}_{2}}}{{{R}_{2}}t}\] or \[\frac{i_{1}^{2}}{4}=\frac{{{H}_{2}}}{4t}\] or \[{{i}^{2}}=\frac{{{H}_{2}}}{t}\] ?(2) From eqs. (1) and (2) \[\frac{{{H}_{2}}}{t}=\frac{{{H}_{1}}}{5t}\] or \[{{H}_{2}}=\frac{{{H}_{1}}}{5}=\frac{10}{5}=2\,kcal\]You need to login to perform this action.
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