A) \[3\,:\,2\]
B) \[3\,:\,8\]
C) \[4\,:\,3\]
D) \[9\,\,:\,\,4\]
Correct Answer: A
Solution :
Key Idea: The rate at which electrical energy is dissipated into other forms of energy is called electric power\[P\]. Electrical power= \[\frac{W}{t}=\frac{V\,it}{t}\] \[\left( V=\,i\,R \right)\] \[\Rightarrow \] \[P\frac{{{V}^{2}}}{R}\] Where \[V\] is potential difference, \[R\] is resistance. Given, \[{{P}_{1}}=40\,W,\] \[{{P}_{2}}=60\,W,\] \[\therefore \] \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\] \[\Rightarrow \] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{P}_{2}}}{{{P}_{1}}}=\frac{60}{40}=\frac{3}{2}\] Note: Higher the wattage of a bulb smaller is the resistance of its filament that is thicker is the filament.
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