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\[4\,\Omega \]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           \[i_{1}^{2}=\frac{{{H}_{1}}}{5t}\]                              ?.(i) 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 \[{{i}^{2}}=\frac{{{H}_{2}}}{t}\]                 ...(ii) From Eqs. (i) and (ii), we get                 \[\frac{{{H}_{2}}}{t}=\frac{{{H}_{1}}}{5t}\] or  \[{{H}_{2}}=\frac{{{H}_{1}}}{5}=\frac{10}{5}=2\text{ }kcal\]