As shown on the figure below a circular loop with radius of

As shown on the figure below, a circular loop with radius of 5cm is located 1 meter away from a long wire carrying current oscillating at 60Hz, I(t) = 10cos(omega t) kA. What is the magnitude of magnetic field in the center of the loop due to the current in straight wire? Estimate the open circuit voltage (infinite load impedance). You can approximate the flux through the loop as a product of the loop area times the magnetic field in the center. Estimate the short circuit current (short circuit load).

Solution

The backfin of a power mosfet has dimensions 1.0 cm x 1.3cm and a thickness of 1.585mm. It is made out of copper. The purpose of the backfin here is to carry away the heat from the si-based chip attached to the backfin (and here burried in a black plastic case). Thus the backfin is (usually) electrically connected to the mosfet. To mount to a grounded case (Aluminum, quite thick, and at room temperature, 23 oC), an electrically insulating, plastic layer of thickness 0.2873mm and of thermal conductivity 90 W/oC/m is placed between the fin and the aluminum. Assume that the aluminum stays throughout at 23 oC degrees. The mosfet will fail catastrophically (thermal runaway) if its temperature gets above 180oC.
(a) If its RDS in the \"on\" state is 78.88 mOhms, what is the maximum current it can safely conduct in steady state in this mount?
(b) Supose the mosfet was operating just at the breaking point...what would then be the temperature at the shared surface between the copper and the plastic layer?