Modeling Circuit Gain/System of Equations

Question

In electronics, circuit gain is modeled by G = Bt/R + R_t ; where R is the value of a resistor, t is the temperature, R_t is the value of R at temperature t, and B is constant. The sensitivity of the circuit to temperature is modeled by S = BR/(R + R_t)². If B= 3.7 and t is 90K (kelvins), use a system of equations in two variables to find values of R and R_t that will result in the values of G = 0.4 and S = 0.001

 

I tried to set up the problem 0.4 = 3.7(90)/R + R_t I got R = -R_t = 832.5 but that answer doesn't work for the next equation. Im pretty sure im going about this all wrong. Any help is appreciated.

Answer 1

1. G = B*t/ (R+R_t)  {Eqn 1}
2. Substituting the values given into Eqn 1 yields:
1. 0.4 = (3.7*90) / (R + R_t)
2. R+R_t = (3.7*90)/ 0.4
3. R+R_t = 832.5   (Eqn 2}
3. S = BR/ (R+R_t)²  {Eqn 3}
4. Substituting the values given into Eqn 3 yields:
1. 0.001 = (3.7*R) / (R+R_t)²
2. Now we can substitute Eqn 2 into the above
3. 0.001 = (3.7*R)/ (832.5)²
4. 0.001* (832.5)² / 3.7 = R
5. R = 187.31
5. Now that you know R, you can plug this value back into Eqn 2 to find R_t