Question

Find the mean temperature rise of a coil when its resistance is 21 Ω and the surrounding temperature is 15°C. It has a resistance of 18 Ω when its mean temperature is 20°C and of 20 Ω when mean temperature is 50°C.

1. 50°C
2. 40°C
3. 30°C
4. 20°C

Answer 1

Correct Answer - Option 1 : 50°C

Concept:

RTD’s are based on the principle that the resistance of a metal increases with temperature.

the relationship between resistance and temperature, may then be expressed as-

R_t = R₀(1+α₀t)

where: Rt = resistance of rtd at temperature t (ohm),

Ro = resistance of rtd at 0 °C (ohm), and

αo = temperature coefficient of resistance (TCR) at 0 °C (per °C)

Calculation:

Given:

 18 Ω when t = 20°C assume temperature coefficient is α.

18 = R₀(1 + α20) ____(1)

20 = R₀(1 + α50)_____(2)

divide equation (1) by equation (2)

\(\frac{{18}}{{20}} = \frac{{1 + 20\alpha }}{{1 + 50\alpha }}\)

10 + 200α = 9 + 450α

\(\alpha = \frac{1}{{250}}\)

\({R_0}\left( {1 + \frac{{20}}{{250}}} \right) = 18\)

\({R_0} = \frac{{18 \times 50}}{{270}} = \frac{{50}}{3}\;{\rm{\Omega }}\)

Now assume temperature is t°C

21 = 12.85 (1 + α.t)

\(\frac{{21}}{{12.85}} - 1 = \frac{t}{{50}}\)

\(21 = \frac{{50}}{3}\left\{ {1 + \frac{1}{{250}}t} \right\}\)

\(\frac{{63}}{{50}} - 1 = \frac{t}{{250}}\)

\(t = \frac{{13}}{{50}} \times 250\)

t = 65°

Since surrounding temperature is 15°C so rise in

Mean temperature = 65° - 15°

= 50°C