A) Increased 8 times
B) Doubled
C) Halved
D) Unchanged
Correct Answer: A
Solution :
Rate of heat developed in the wire= \[P=\frac{{{V}^{2}}}{R}\] \[{{R}_{1}}=\frac{\rho L}{A}=\frac{\rho L}{\pi {{r}^{2}}}\] \[{{P}_{1}}=\frac{{{V}^{2}}}{{{R}_{1}}}\] \[{{R}_{2}}=\frac{\rho \frac{L}{2}}{\pi {{(2r)}^{2}}}=\frac{\rho L}{\pi 8{{r}^{2}}}=\frac{{{R}_{1}}}{8}\] \[{{P}_{2}}=\frac{V}{{{R}_{1}}}=\frac{8V}{{{R}_{1}}}\] \[{{P}_{2}}=8{{P}_{1}}\]
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