The resistance of thermistor A and B at 373 K are found to be 135 - and 265 - respectively- The resistance of each of the themister at 298 K is 2k - The ratio of material constant of thermistor A to that of thermistor B will be approximately

The resistance of thermistor at any temperature T (K) is given by: R_T = R_0 exp β{1T 1T_0} R_0 = Resistance at T_0 K R_T = Resistance at T K β nbsp;= Mat ...

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The resistance of thermistor A and B at 373 K are found to be $135 Ω$ and $265 Ω$ respectively. The resistance of each of the themister at 298 K is $2 k Ω .$ The ratio of material constant of thermistor A to that of thermistor B will be approximately

0.749

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0.500

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1.000

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1.330

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Solution

The correct option is D 1.330
The resistance of thermistor at any temperature T (K) is given by:

$R_{T} = R_{0} e x p β {\frac{1}{T} - \frac{1}{T_{0}}}$

$R_{0} = R e s i s t a n c e a t T_{0} K$

$R_{T} = R e s i s t a n c e a t T K$

$β = M a t e r i a l c o n s t a n t (K)$

$∵ A s p e r g i v e n d a t a$

$R_{A | (373 K)} = 2 k e x p β_{A} {\frac{1}{373} - \frac{1}{298}}$

$\Rightarrow 135 Ω = 2 k e x p β_{A} {\frac{1}{373} - \frac{1}{298}}$

$\Rightarrow β_{A} = 3995.298$

$s i m i l a r l y$

$R_{B | (373 K)} = 2 k e x p β_{B} {\frac{1}{373} - \frac{1}{298}} = 265$

$\Rightarrow β_{B} \approx 2995.66$

$Then the required ratio$

$\frac{β_{A}}{β_{B}} = \frac{3995.298}{2995.66} \approx 1.33$

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The resistance of thermistor A and B at 373 K are found to be 135 Ω and 265 Ω respectively. The resistance of each of the themister at 298 K is 2kΩ. The ratio of material constant of thermistor A to that of thermistor B will be approximately

The resistance of thermistor A and B at 373 K are found to be $135 Ω$ and $265 Ω$ respectively. The resistance of each of the themister at 298 K is $2 k Ω .$ The ratio of material constant of thermistor A to that of thermistor B will be approximately