Question

The power of the heater is $1000W$ at ${1000}^{\circ }C$. What will be its power at ${4000}^{\circ }C$?
Given, temperature coefficient of resistance of heater-wire is $1.4\times {10}^{-4}{}^0{C}^{-1}$.

• A. $1.42\times {10}^{3}W$
• B. $1.3\times {10}^{3}W$
• C. $9.68\times {10}^{3}W$
• D. $1.08\times {10}^{3}W$

Answer 1

Answer: (A)

$1.42\times {10}^{3}W$

Assumption, same current flows through the heater in both the cases.

By Joule's Law, $P=I^{2}R$

But, $R=R_o(1+\alpha (T-T_o\left)\right)$

hence, $P=I^2{R}_o(1+\alpha (T-T_o\left)\right)$

Ratio of powers in two cases is:

$\frac{P_{4000}}{P_{1000}}=\frac{1+\alpha (4000-1000)}{1+\alpha (1000-1000)}$

$P_{4000}=1000\times (1+3000\times 1.4\times {10}^{-4})$

$P_{4000}=1.42\times {10}^{3}W$