(a) Express and in terms of the other parameters defined above. · OlympiadBench #1503

Physics · electromagnetism

Problem

(a) Express

V_{1}

and

V_{2}

in terms of the other parameters defined above. Given constants: A resistor is made of a material which undergoes a phase transition so that its resistance takes one of the two values,

R_{1}

if its temperature is smaller than

T_{c}

, and

R_{2}>R_{1}

if the temperature is larger than

T_{c}

. <image_1> This resistor is connected to a voltage source through an inductor of inductance

L

. It appears that if the applied voltage

V

is between two critical values,

V_{1}<V<V_{2}

, the temperature of the resistor starts oscillating. Assume that (i) the heat flux

P

from the resistor to the ambient medium is given by

P=\alpha\left(T-T_{0}\right)

, where

\alpha

is a constant,

T

denotes the temperature of the resistor, and

T_{0}

is the ambient temperature; (ii) the geometrical size of the resistor is so small that it will reach a thermal equilibrium much faster than the characteristic time

L / R_{2}

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