A) \[r\]
B) \[r/2\]
C) \[2r\]
D) infinite
Correct Answer: A
Solution :
\[E=i(R+r)\] \[\Rightarrow \] \[V=i(R+r)\Rightarrow i=\frac{V}{R+r}\] Heat produced\[H={{\left( \frac{V}{r+R} \right)}^{2}}R\] For maximum heat \[\frac{dH}{dR}=0\] Differentiating w.r.t.\[R\], we get \[0=\frac{d}{dR}{{V}^{2}}[R{{(r+R)}^{-2}}]\] \[{{(r+R)}^{-2}}-2R{{(r+R)}^{-3}}=0\] \[0=1-\frac{2R}{r+R}\] So, \[R=r\]You need to login to perform this action.
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