at A conductor with resistance R carries a constant positive current , and hence dissipates a power P - RP. "This causes

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At A Conductor With Resistance R Carries A Constant Positive Current And Hence Dissipates A Power P Rp This Causes 1 (39.92 KiB) Viewed 58 times

at A conductor with resistance R carries a constant positive current , and hence dissipates a power P - RP. "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 + UTP dt where a > 0.6> 0 are thermal coefficients and P is the power dissipated in the conductor The resistance of the conductor changes with temperature according to R Roll+T) where the constante is called the resistance temperature coefficient of the conductor and Ro0 is the resistance of the conductor at ambient temperature Consider a metal wire, for which e > 0. If the current is smaller than a critical value tari. the temperature T converges to a steady-state value as 00. If the current is larger than this critical value of current, then the temperature T goes to const goes too. (In practice, the temperature increases until the conductor is destroyed). This phenomenon is called thermal runaway Asume a = 13,04 WPC, RO = 100 and e=0010C Find the critical value for 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