Question

At room temperature (27.0 °C) the resistance
of a heating element is 100 22. What is the
temperature of the element if the resistance is
found to be 117 42, given that the temperature
coefficient of the material of the resistor is
1.70 x 10-4 °C-1
(A) 1207°C
(B) 0.1207°C
(C) 1027°C
(D) 1027 x 10-4 (°C)​

Answer 1

Question:

At room temperature (27 °C) the resistance of a heating element is 100 Ω.

What is the temperature of the element if the resistance is found to be 117 Ω given that the temperature coefficient of the material of the resistor is 1.70  × 10⁻⁴ °C⁻¹.

Answer:

Option C: 1027 °C

Explanation:

Given:

• Initial temperature = 27°C
• Initial resistance = 100 Ω
• Final resistance = 117 Ω
• Temperature coefficient = 1.70  × 10⁻⁴ °C⁻¹

To Find:

• The final temperature

Solution:

Here we have to find the temperature of the element at 117 Ω.

We know that temperature coefficient of an element is given by,

$\tt \alpha=\dfrac{R-R_0}{R_0(t-t_0)}$

where α is the temperature coefficient, R is the final resistance, R₀ is the initial resistance, t is the final temperature and t₀ is the initial temperature.

Substitute the data,

$\tt 1.70\times 10^{-4}=\dfrac{117-100}{100(t-27)}$

$\tt 1.70\times 10^{-2}=\dfrac{17}{t-27}$

$\tt 0.017t-0.459=17$

$\tt 0.017t=17+0.459$

$\tt 0.017t=17.459$

$\tt t=\dfrac{17.459}{0.017}$

$\tt t=1027\: ^oC$

Hence the final temperature of the element is 1027°C.

Therefore option C is correct.

Answer 2

Given :-

Temperature = 27.0⁰ C

Resistance (Initial) = 100 Ω

Resistance (Final) = 117 Ω

To Find :-

Final temperature

Solution :-

$\sf Temperature_{(coefficient)} = \dfrac{Final_{(Resistance)} - Initial_{(Resistance)}}{Initial_{(Resistance)}\times( Temperature_{(Final)} - Temperature_{(Initial)})}$

Now

$\sf 1.7 \times 10^{-4} = \dfrac{117 - 100}{100(Temperature_{(final)} - 27)}$

$\sf 1.7 \times 10^{-4} = \dfrac{17}{100(Temperature_{(Final)} - 27)}$

$\sf1.7 \times 10^{-2} = \dfrac{17}{Temperature_{(Final)} - 27}$

$\sf 0.017 = \dfrac{17}{T_{(F)} - 27}$

$\sf 0.017 t - 0.459 = 17$

$\sf 0.017t = 17.459$

$\sf t=1027$