Question 257: Current Electricity

Question

Model a torch battery of length $$l$$ to be made up
of a thin cylindrical bar of radius ‘a’ and a
concentric thin cylindrical shell of radius ‘b’
filled in between with an electrolyte of
resistivity $$\rho $$ (see figure). If the battery is
connected to a resistance of value R, the
maximum Joule heating in R will take place for :

Accepted Answer

Internal resitance of battery
$$\int {dr}  = \int\limits_a^b {{{ho dr} \over {2\pi rl}}} $$
$$ \Rightarrow $$ r = $${{ho  \over {2\pi l}}\ln {b \over a}}$$
Power in external resistance P
R
= $${\left( {{ \in  \over {r + R}}} ight)^2}R$$
Maximum Power in external resistance is generated when it is equal to internal resistance of battery. So P
R
is maximum when r = R.
$$ 	herefore $$ R = $${{ho  \over {2\pi l}}\ln {b \over a}}$$

Answer

$$R = {{2\rho } \over {\pi l}}\ln \left( {{b \over a}} \right)$$

Answer

$$R = {\rho  \over {\pi l}}\ln \left( {{b \over a}} \right)$$

Answer

$$R = {\rho  \over {2\pi l}}\ln \left( {{b \over a}} \right)$$

Answer

$$R = {\rho  \over {2\pi l}}\left( {{b \over a}} \right)$$

Current Electricity

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