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. |
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