Question #42127

A thermistor has a temperature-dependent resistance given by $R(T) = R_0 e^{\beta/T}$, where $T$ is the absolute temperature in Kelvin. It is given that $R_0 = 10\ \Omega$ and $\beta = 300 \ln(3)\ \text{K}$. The thermistor is connected in series with an inductor of inductance $L = 0.4\ \text{H}$ and an AC voltage source $V(t) = 100 \sin(100t)\ \text{V}$. The temperature is measured using a faulty linear scale $^\circ X$, on which the freezing and boiling points of water are $10^\circ X$ and $110^\circ X$, respectively. In steady state, the thermistor reaches a constant operating temperature measured as $37^\circ X$, while the surrounding environment is at $7^\circ X$. Assuming Newton's law of cooling holds, what is the thermal dissipation constant $K$ of the thermistor?