Question

5. Heating a resistor in an RC circuit. A simple RC circuit is made from a cylindrical capacitor and a thermally isolated resistor connected to a 10,000 V DC power supply, as in Figure P31.73 on Page 919 The capacitor is initially uncharged. The switch is then closed and the capacitor begins to charge. Find an expression for the temperature of the resistor versus time since closing the switch if the resistor's initial temperature was 20°C. Assume that the resistor heats instantly as energy is delivered to it. Sketch the function by hand including at least 5 calculated points. Only extend the time axis to about 1 time constant (t-RC). Try to be neat with the sketch. Include a horizontal line showing the asymptote. You are not required to use graph paper, although that would be nice. Take all calculations to only two significant figures. Does the temperature of the resistor have the same time dependence as the current? Why or why not? Use the following data along with equations for resistance and capacitance available from the book: Cylindrical Capacitor inner radius is 99.9% as large as the outer radius Length is 20 cm The space is filled with a dielectric, K-35 Resistor Resistance is established by a thin film of length 10 cm, thickness 0.10 μm, width 10 μm Resistivity 1.0x 10-4 Ω·m and temperature stabilized Specific Heat 300 J/kg.°C Mass 3.0 g

Can you please provide every step with an explanation as well? Thank you very much!

Answer 1