Current Electricity 3 Question 8
7. Two bars of radius $r$ and $2 r$ are kept in contact as shown. An electric current $I$ is passed through the bars. Which one of following is correct?
$(2006,3 M)$
(a) Heat produced in bar $B C$ is 4 times the heat produced in bar $A B$
(b) Electric field in both halves is equal
(c) Current density across $A B$ is double that of across $B C$
(d) Potential difference across $A B$ is 4 times that of across $B C$
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Solution:
- Current flowing through both the bars is equal.
Now, the heat produced is given by
$$ \begin{aligned} H=I^{2} R t \quad & \text { or } H \propto R \quad \text { or } \quad \frac{H _{A B}}{H _{B C}}=\frac{R _{A B}}{R _{B C}} \\ & =\frac{(1 / 2 r)^{2}}{(1 / r)^{2}} \quad \text { as } R \propto \frac{1}{A} \propto \frac{1}{r^{2}} \\ & =\frac{1}{4} \\ \text { or } \quad H _{B C} & =4 H _{A B} \end{aligned} $$
