Two bars of equal resistivity `rho` and radius 'r' and '2r' are kept in contact as show. An electric current is passed through the bars. Which one of the following is correct ?

Options

A. Heat produced in bar BC is 4 time the heat produced in bar AB
B. Electric field in both halves is equal
C. Current densit across AB is double that of across BA
D. Potential difference across AB is 4 time that of across BC

Answer

A

Explanation

Current flowing through both the bars is equal. Now, the heat produced is given by
`H = l^(2)Rt`
or `H prop R`
or `(H_(AB))/(H_(BC))=(R_(AB))/(R_(BC))=((1//2r)^(2))/((1//r)^(2))=(1)/(4) " "(because R prop (1)/(A) prop (1)/(r^(2)))`
or `H_(BC)= 4 H_(AB)`
Therefore heat produced in bar BC is 4 times the heat produced in bar AB