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 \[5\,\Omega =10\,kcal\] 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            \[{{H}_{2}}=\frac{{{H}_{1}}}{5}=\frac{10}{5}=2\,kcal\]