Question

The same mass of copper is drawn into two wires A and B or radii r and 3r respectively. They are connected in series, and electric current is passed. The ratio of the heat produced in A and B is

• A. 1 : 9
• B. 1 : 81
• C. 81 : 1
• D. 9 :1

Answer 1

The correct option is C 81 : 1

$H=I^{2}RT$

$=I^2\left(p\frac{l}{A}\right)T$

$=I^2(p\frac{l}{A}\times \frac{A}{A})T$

$=I^2\left(p\frac{V}{A^2}\right)T$

$V=A\times l$

$\Rightarrow H\propto \frac{1}{r^4}$

$\frac{H_1}{H_2}={\left(\frac{r_2}{r_1}\right)}^4$

$={\left(\frac{3}{1}\right)}^4$

$=\frac{81}{1}$.