question_answer

When a certain current is passed in the circuit as shown in figure, 10 kcal of heat is produced in 5\[\Omega \] resistance. How much heat is produced in \[\Omega \] resistance?

A)  4 kcal            

B)  2 kcal

C)  5 kcal            

D)  3 kcal

Correct Answer: B

Solution :

 Heat produced in \[5\,\Omega =10\text{ }kcal\] 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 \[{{H}_{2}}+\frac{{{H}_{1}}}{5}=\frac{10}{5}=2\,kcal\]