Problem $3(2$ points$)$ A thermistor has a resistance of $250$ k$$ at $0$C$.$ The thermistor is introduced in a voltage divider circuit to measure temperature. At a temperature of $80$C the voltage output is $2\mathrm{.}25$ V$.$ The reference resistor $($R$1)$ in the voltage divider is R$1=100$ k$$ and the input voltage is $5$ V$.$ a$)$ Calculate the thermistor material constant $.$ b$)$ Now that you have $,$ we place the thermistor in a water bath at an unknown temperature. Using the same reference resistor R$1,$ the voltage output from the divider circuit is $3\mathrm{.}5$ V$.$ What is the temperature of the water bath? c$)$ Indicate step by step how you would calculate the uncertainty of this temperature if the resolution of the voltmeter is $0\mathrm{.}01$ V and its accuracy is $2\%$ of $10$V$.($Sol: a$)862\mathrm{.}06$ K b$)618\mathrm{.}3$ K $)$