Question

A 2m long wire of resistance $4\Omega$ and diameter 0.64 mm is coated with plastic insulation of thickness 0.06 mm. A current of 5 A flows through the wire. Find the temperature difference across the insulation in the steady state( in c). Thermal conductivity of $plastic=0.16\times {10}^{-2}cal/sc{m}^{\circ }C$.

Answer 1

Power produced $=4\times 5\times 5=100J/s=\frac{100}{4.2}cal/s$

So, $\frac{100}{4.2}=\frac{△\theta }{\frac{l}{kA}}=\frac{△\theta }{\frac{0.06\times {10}^{-1}}{0.16\times {10}^{-2}\times 40.192}}[2\pi r\times 200]=2\times 3.14\times 0.032\times 200=40.192]\Rightarrow △\theta =2.232℃$