Answer to Question #157769 in Electric Circuits for YAHIA

Question

)For a certain thermistor, its resistance at 32 o F is known to be 9 KΩ. And at 212 o F is 2KΩ. Find its resistance at 77 o F.

Answer 1

R_o = 9 KΩ

T_o  = 32 ^o F     is   ^o C + 273 = 273 ^o K

 R_T1 = 2 KΩ

T₁   = 212 ^o F   is (212 - 32) x $\frac{5}{9}$  ^o C + 273 = 100 + 273 = 373 ^o K

R_T2 = ? KΩ

T₂ = 77 ^o F      is (77- 32) x $\frac{5}{9}$  ^o C + 273 = 25 + 273 = 298 ^o K

$R_1 = R_oe^{\large \beta(\frac{1}{T_1}-\frac{1}{T_2})}$

$2 = 9e^{\large\beta(\frac{1}{373}-\frac{1}{273})}$     $ln\frac{2}{9} = \beta(\frac{1}{373}-\frac{1}{273}) \to \beta = -1.5\large\frac{373*273}{-100} =$ 1531.58K

$R_2 = 2e^{1531.57(\large\frac{1}{298}-\frac{1}{373})} = 5.62K\varOmega$