question_answer

                Which  of the four resistances P, Q, R and S generate the greatest amount of heat when a current flows from A to B?     [JEE Main Online Paper ( Held On 23  April 2013 )

A)                   Q                                          

B)                                          S

C)                                          P                                          

D)                                          R

Correct Answer: B

Solution :

                     \[{{R}_{1}}=P+Q=2\Omega +4\Omega =6\Omega \] \[{{R}_{2}}=R+S=1\Omega +2\Omega =3\Omega \] \[{{I}_{1}}{{R}_{1}}={{I}_{2}}{{R}_{2}}\] \[{{I}_{1}}=\frac{{{R}_{2}}}{{{R}_{1}}}{{I}_{2}}=\frac{3}{6}{{I}_{2}}=\frac{{{I}_{2}}}{2}\] or\[{{I}_{2}}=2{{I}_{1}}\] Heat flow \[H={{I}^{2}}Rt\] For\[Q,{{H}_{Q}}=I_{1}^{2}Qt=\frac{I_{2}^{2}}{4}\times 4t=I_{2}^{2}t\]  For\[QS,{{H}_{S}}=I_{2}^{2}St=I_{2}^{2}.2t=2I_{2}^{2}t\] \[\therefore \]Greatest amount of heat generated by S.