Two bars of radius r and 2r are kept in contact as shown. An electric current I is passed through the bars. Which one of following is correct ?

Question

Two bars of radius r and 2r are kept in contact as shown. An electric current I is passed through the bars. Which one of following is correct ? (A) Heat produced in bar BC is 4 times the heat produced in bar AB (B) Electric field in both halves is equal (C) Current density across AB is double that of across BC (D) Potential difference across AB is 4 times that of across BC

Tardigrade Admin · Accepted Answer

Current flowing through both the bars is equal.
Now, the heat produced is given by

H = I^{2} Rt orH \propto R or \frac{H _{A B}}{H _{BC}} = \frac{R _{A B}}{R _{BC}}

= \frac{( 1/2 r ) ^{2}}{( 1/ r ) ^{2}} (a s R \propto \frac{1}{A} \propto \frac{1}{r ^{2}})

= \frac{1}{4} or H_{BC} = 4 H_{A B}

Q. Two bars of radius r and 2r are kept in contact as shown. An electric current I is passed through the bars. Which one of following is correct ?

Heat produced in bar BC is 4 times the heat produced in bar AB

Electric field in both halves is equal

Current density across AB is double that of across BC

Potential difference across AB is 4 times that of across BC

Current flowing through both the bars is equal. Now, the heat produced is given by H=I2RtorH∝RorHBC​HAB​​=RBC​RAB​​ =(1/r)2(1/2r)2​(asR∝A1​∝r21​) =41​orHBC​=4HAB​

Q. 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 ?

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^{2} Rt orH \propto R or \frac{H _{A B}}{H _{BC}} = \frac{R _{A B}}{R _{BC}}$
$= \frac{( 1/2 r ) ^{2}}{( 1/ r ) ^{2}} (a s R \propto \frac{1}{A} \propto \frac{1}{r ^{2}})$
$= \frac{1}{4} or H_{BC} = 4 H_{A B}$