A) 15 minutes
B) 12 minutes
C) 10 minutes
D) 8 minutes
Correct Answer: C
Solution :
\[H=\frac{{{V}^{2}}}{R}t\] Since supply voltage is same and equal amount of heat will produce, therefore \[\frac{{{R}_{1}}}{{{t}_{1}}}=\frac{{{R}_{2}}}{{{t}_{2}}}\] or \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{t}_{1}}}{{{t}_{2}}}\] .....(i) But \[R\propto l\]Þ \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\] .....(ii) By (i) and (ii), \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{t}_{1}}}{{{t}_{2}}}\] .....(iii) Now \[{{l}_{2}}=\frac{2}{3}\,\,{{l}_{1}}\] Þ \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{3}{2}\] \ By equation (iii), \[\frac{3}{2}=\frac{15}{{{t}_{2}}}\] Þ \[{{t}_{2}}=10\,\,\]minutes
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