Question 252428
the 2 formulas you have to work with are:


{{{G = ((B*t) / (R + R[t]))}}}


and:


{{{S = (B*R / ((R + R[t])^2))}}}


R is the nominal value of a resistor.  
R[t] is the value of the resistor at a certain temperature.
B is a constant.
t is the temperature using the Kelvin Scale.
S is the sensitivity of the circuit to temperature.


Your problem is:


"If B = 3.7 and "t" is 90K (Kelvin), find the values of R and Rt that will make G = .4 and S = .001.  (Answer: R= 187 , Rt = 645)"


We have:


B = 3.7
t = 90
G = .4
S = .001


We want to find R and R[t].


The first formula is:


{{{G = ((B*t) / (R + R[t]))}}}


Substituting in this formula gets:


{{{.4 = ((3.7*90) / (R + R[t]))}}}


We divide both sides of this equation by .4 and we multiply both sides of this equation by (R + R[t]) to get:


{{{(R + R[t]) = ((3.7*90) / .4)}}}


We solve for (R + R[t] to get:


{{{(R + R[t]) = 832.5}}}


The second formula is:


{{{S = ((B*R) / ((R + R[t])^2)))}}}


We substitute in this formula to get:


{{{.001 = ((3.7*R) / (832.5^2))}}}


S and B were given.
R + R[t] was calculated from the first equation.


We multiply both sides of this equation by (832.5)^2 and we divide both sides of this equation by 3.7 to get:


{{{R = (.001 * (832.5)^2)/3.7)}}}


We solve for R to get R = 187.325


Since R + R[t] = 832.5, this means that R[t] = 832.5 - 187.325 = 645.1875


we round these out to get:


R = 187
R[t] = 645


This agrees with the answers you provided.


The key was solving for R + R[t] together in the first equation and then using that value to solve for R in the second equation.


Once we knew R, getting R[t] was a simple matter of subtraction.


I think that's what you were looking for.


Let me know if otherwise.