- A Conductor With Resistance R Carries A Constant Positive Current And Hence Dissipates A Power P Ri This Causes The 1 (71.42 KiB) Viewed 32 times
A conductor with resistance R carries a constant positive current , and hence dissipates a power P = Ri? This causes the conductor to heat up above the ambient temperature. Let T denote the temperature of the conductor above the ambient temperature at time t. T satisfies the equation dT + 7 =P dt where a > 0, b>0 are thermal coefficients and P is the power dissipated in the conductor. The resistance R of the conductor changes with temperature according to: R = R. (1+T) where the constant c is called the resistance temperature coefficient of the conductor and Ro > 0 is the resistance of the conductor at ambient temperature. Consider a metal wire, for which c>0. If the current i is smaller than a critical value crie the temperature T converges to a steady-state value as t . If the current is larger than this critical value of current, then the temperature T goes to const goes to o. (In practice, the temperature increases until the conductor is destroyed). This phenomenon is called thermal runaway. Assume a = 15°C, b = 0.4 W/°C , Ro = 19 and c = 0.010/°C Find the critical value ferit. above which thermal runaway occurs. Enter your answer, in Amperes (A), to 2 decimal places in the box below. Enter the numerical value only without units