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 ONLINE 23-04-2013]

A)             Q

B) S

C)             P

D) R

Correct Answer: B

Solution :

[b]

\[{{R}_{1}}=P+Q=2\Omega +4\Omega =6\Omega \]

\[{{R}_{2}}=R+S=1\Omega +2\Omega =3\Omega \]

\[{{I}_{1}}{{R}_{1}}={{I}_{2}}{{R}_{2}}\]

\[{{I}_{1}}=\frac{{{R}_{2}}}{{{R}_{1}}}{{I}_{2}}=\frac{3}{6}{{I}_{2}}=\frac{{{I}_{2}}}{2}\] 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.