A) 6min
B) \[12.5min\]
C) 24min
D) \[7.5min\]
Correct Answer: A
Solution :
For first Filament \[H=\frac{{{V}^{2}}}{{{R}_{1}}}{{t}_{1}}\] or \[{{R}_{1}}=\frac{{{V}^{2}}}{H}{{t}_{1}}\] ?.(i) For second filament \[H=\frac{{{V}^{2}}}{{{R}_{P}}}{{t}_{p}}\] or \[{{R}_{p}}\frac{{{V}^{2}}}{H}{{t}_{2}}\] ?..(ii) If placed in parallel \[H=\frac{{{V}^{2}}}{{{R}_{P}}}{{t}_{p}}\] or \[Rp=\frac{{{V}^{2}}}{H}{{t}_{p}}\] ?..(iii) If the two heater are connected in parallel then, \[\frac{1}{{{R}_{p}}}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}\] ?..(iv) Using equation (i), (ii) and (u0, equation (iv) \[\frac{H}{{{V}^{2}}{{t}_{p}}}=\frac{H}{{{V}^{2}}{{t}_{1}}}+\frac{H}{{{V}^{2}}{{t}_{2}}}\] Here, \[{{t}_{1}}=10\min ,\] and \[{{t}_{2}}=15min\] \[\frac{1}{{{t}_{p}}}=\frac{1}{10}+\frac{1}{15}\] \[\Rightarrow \] \[{{t}_{p}}=6\] minutes
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