The power of a heater is 500 W at a temperat | vedclass

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(A) The power of a heater is given by $P = \frac{V^2}{R}$. Assuming the voltage $V$ remains constant,$P \propto \frac{1}{R}$.The resistance at tempera

Vedclass · Accepted Answer

$611$

Vedclass · Answer

(A) The power of a heater is given by $P = \frac{V^2}{R}$. Assuming the voltage $V$ remains constant,$P \propto \frac{1}{R}$.The resistance at temperature $T$ is given by $R_T = R_0(1 + \alpha T)$.Therefore,$\frac{P_{200}}{P_{800}} = \frac{R_{800}}{R_{200}} = \frac{R_0(1 + \alpha 	imes 800)}{R_0(1 + \alpha 	imes 200)}$.Substituting the given values: $\alpha = 4 	imes 10^{-4} \ ^oC^{-1}$,$P_{800} = 500 \ W$.$\frac{P_{200}}{500} = \frac{1 + (4 	imes 10^{-4} 	imes 800)}{1 + (4 	imes 10^{-4} 	imes 200)} = \frac{1 + 0.32}{1 + 0.08} = \frac{1.32}{1.08}$.$P_{200} = 500 	imes \frac{1.32}{1.08} \approx 611.11 \ W$.Rounding to the nearest integer,the power is $611 \ W$.

The power of a heater is $500 \ W$ at a temperature of $800 \ ^oC$. What will be its power at $200 \ ^oC$ in $W$? Given $\alpha = 4 \times 10^{-4} \ ^oC^{-1}$.

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