Question 331: 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 :
![](https://imagex.cdn.examgoal.net/jgy2xukf145qx7/03eee02c-0615-4af7-b50b-77d38a910a1b/200265b0-f5c2-11ea-8293-3b6cc591631c/file-jgy2xukf145qx8-269w.png)

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 = ${{ho  \over {2\pi l}}\ln {b \over a}}$
![](https://imagex.cdn.examgoal.net/1kir17fb7/fc0f09ba-101a-402c-bc45-a899fa5de20f/9a4b0040-3f67-11eb-9d37-c12600f3cc12/file-1kir17fb8-326w.png)

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

Choose the correct answer: