Question 32: Current Electricity

Question

The resistance of a heating element is found to be $120 \Omega$ at room temperature which is $20^{\circ} \mathrm{C}$. If the temperature coefficient of the material of the resistor is $1.6 	imes 10^{-4} C^{-1}$ and the resistance is found to be $160 \Omega$, the temperature of the element is:

Accepted Answer

We know that for a metal resistor
$$R = R_0\bigl[1 + \alpha\,(T - T_0)\bigr]$$
where
Ã¢ÂÂ¢ $R_0=120\;\Omega$ at $T_0=20^\circ\mathrm C$
Ã¢ÂÂ¢ $\alpha=1.6	imes10^{-4}\;^\circ\mathrm C^{-1}$
Ã¢ÂÂ¢ $R=160\;\Omega$ at the unknown $T$.
Compute the fractional change in resistance:
$$\frac{R}{R_0}-1 = \frac{160}{120}-1 = \frac{4}{3}-1 = \frac{1}{3}\approx0.3333.$$
Solve for the temperature rise $\Delta T = T - T_0$:
$$\Delta T = \frac{\frac{R}{R_0}-1}{\alpha}             = \frac{0.3333}{1.6	imes10^{-4}}             \approx2083.3\;^\circ\mathrm C.$$
Therefore the elementÃ¢ÂÂs absolute temperature is
$$T = T_0 + \Delta T          = 20 + 2083.3          \approx2103.3\;^\circ\mathrm C.$$
Since $2103^\circ\mathrm C$ isnÃ¢ÂÂt among the given choices but $2083^\circ\mathrm C$ appears (Option B), the intended answer is
Option B: 2083 ÃÂ°C.

Answer

$1203^{\circ} \mathrm{C}$

Answer

$2083^{\circ} \mathrm{C}$

Answer

$2310^{\circ} \mathrm{C}$

Answer

$2013^{\circ} \mathrm{C}$

Current Electricity

The resistance of a heating element is found to be 120 \Omega at room temperature which is 20^{\circ} \mathrm{C}. If the temperature coefficient of the material of the resistor is 1.6 \times 10^{-4} C^{-1} and the resistance is found to be 160 \Omega, the temperature of the element is:

Choose the correct answer: