The resistance of a typical carbon film resistor will decrease by about 0.05% of

Question

The resistance of a typical carbon film resistor will decrease by about 0.05% of its stated value
for each degree Celsius increase in temperature. Silicon is very sensitive to temperature, decreasing its resistance by about 7% for each degree Celsius increase in temperature. This can
be a serious problem in modern electronics and computers since silicon is the primary material
from which many electronic devices are fabricated.
Create a proper plot to compare a carbon film resistor with a resistor fabricated from specially
doped silicon (“doped” means impurities such as phosphorus or boron have been added
to the silicon).
For relatively small temperature differences from the reference temperature, this process is
essentially linear. Use polyfit to determine linear models for each data set. For each model,
add the trendline and the associated trendline equation to the graph. Use an appropriate location
for the equations to clearly associate them with the correct trendline.
Resistance (R) []
Temperature (T)[°C] Carbon Film Doped Silicon
15 10.050 10.15
20 10.048 9.85
25 10.045 9.48

Need to be done in MATLAB

Explanation / Answer

Code:

Temp = [15 20 25];
Carbon = [10.05 10.048 10.047]
Silicon = [10.15 9.85 9.48]
sigma_xy=0
sigma_x = 0
sigma_x_2 = 0
sigma_y=0
for i=1:length(Temp)
   sigma_xy = sigma_xy + (Temp(i)* Carbon(i))
   sigma_x = sigma_x + Temp(i)
   sigma_y = sigma_y + Carbon(i)
   sigma_x_2 = sigma_x_2 + (Temp(i)* Temp(i))
end
n=length(Temp)
slope_carbon = ((n*sigma_xy) - (sigma_x * sigma_y)) / ((n*sigma_x_2)- (sigma_x*sigm_x))
offset_carbon = (sigma_y - ((slope_carbon )* sigma_x))/n
sigma_y=0
sigma_xy=0
sigma_x = 0
sigma_x_2 = 0
for i=1:length(Temp)
   sigma_xy = sigma_xy + (Temp(i)* Silicon(1))
   sigma_x = sigma_x + Temp(i)
   sigma_y = sigma_y + Silicon(i)
   sigma_x_2 = sigma_x_2 + (Temp(i)* Temp(i))
end
n=length(Temp)
slope_silicon = ((n*sigma_xy) - (sigma_x * sigma_y)) / ((n*sigma_x_2)- (sigma_x*sigm_x))
offset_silicon = (sigma_y - ((slope_carbon )* sigma_x))/n
for x=1:25
y_carb= (slope_carbon *x) +offset_carbon
y_sili= (slope_silicon *x) +offset_silicon
end
plot(y_carb,y_sili)

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