Three otherwise identical capacitors, C1, C2, and C3, are filled with air, water

Question

Three otherwise identical capacitors, C1, C2, and C3, are filled with air, water at 20C, and titanium dioxide (r 100) for the circuit shown. Find the relative charges across the capacitors in each case. If the permittivity of TiO2 is constant, how does the answer chnage if the water temperature is raised to 100C? How could you use these answers to make a thermometer? Which configuration would be the most sensitive to the temperature change? Would the termometer work if C2 had a fixed separation that you put across an earlobe?

Explanation / Answer

Water 88, 80.1, 55.3, 34.5 (0, 20, 100, 200 °C) (Dielectric coefficients) Capacitance is proportianal to Dielectric coefficient C2= 80.1 C1 C3=100 C1 As the temperature of water is increasing, the capacitance of C2 is increasing .. configuration 1: total capacitance= C1+C2+C3 = C1(181.1) configuration 2: C= C1*(C2+C3)/ C1+C2+C3 Configuration 3: 1/C = 1/C1 + 1/C2 + 1/C3 the first configuration will have the highest sensitivity.. You can check dC/dC2 for all the three configurations.. in the first case, C is increasing directly with C2.. When the temperature is increased to 100C, C2 = 55.3 C1 The first configuration can be used as a thermometer, because it's capacitance is increasing linearly with capacitance of C2..

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