Question

if paheli has taken a wire of 10 cm and boojho has taken of 5 cm (both of same material) then will the heat produced by both the wire will remain same?explain
if two wires are of different thickness then will the heat produced will be same?explain

Answer 1

$$\begin{gathered} \mathrm{Heat}\mathrm{produced}\mathrm{in}\mathrm{a}\mathrm{current}\mathrm{carrying}\mathrm{wire}: \\ \mathrm{H}={\mathrm{I}}^2\mathrm{Rt} \\ ={\mathrm{I}}^2\left(\frac{\mathrm{\rho L}}{\mathrm{A}}\right)\mathrm{t} \\ =\frac{{\mathrm{\rho I}}^2\mathrm{Lt}}{{\mathrm{\pi r}}^2} \\ \mathrm{where} \\ \mathrm{\rho }=\mathrm{Resistivity}\mathrm{of}\mathrm{the}\mathrm{wire} \\ \mathrm{I}=\mathrm{Current}\mathrm{through}\mathrm{the}\mathrm{wire} \\ \mathrm{L}=\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{wire} \\ \mathrm{t}=\mathrm{Time}\mathrm{of}\mathrm{flow}\mathrm{of}\mathrm{current} \\ \mathrm{r}=\mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{wire} \\ \mathrm{Case}\mathrm{I}:(\mathrm{Same}\mathrm{material},\mathrm{but}\mathrm{different}\mathrm{lengths}-10\mathrm{cm},5\mathrm{cm}) \\ \mathrm{Heat}\mathrm{produced}\mathrm{is}\mathrm{directly}\mathrm{proportional}\mathrm{to}\mathrm{length}. \\ \mathrm{Hence},\mathrm{more}\mathrm{heat}\mathrm{is}\mathrm{produced}\mathrm{in}\mathrm{longer}\mathrm{wire}\mathrm{of}\mathrm{length}10\mathrm{cm} \\ \mathrm{Case}\mathrm{II}:(\mathrm{Different}\mathrm{thickness}) \\ \mathrm{Heat}\mathrm{produced}\mathrm{is}\mathrm{inversely}\mathrm{proportional}\mathrm{to}\mathrm{square}\mathrm{of}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{crosssection}, \\ \mathrm{that}\mathrm{is},\mathrm{inversely}\mathrm{proportional}\mathrm{to}\mathrm{thickness}. \\ \mathrm{Hence},\mathrm{more}\mathrm{heat}\mathrm{is}\mathrm{produced}\mathrm{in}\mathrm{thinner}\mathrm{wire}. \end{gathered}$$