12 copper solder Plastic cover 11 13 Oh NO! Your brand new RTX4090 just melted one of its connectors! After some investigation, you believe that the issue was caused by a loose connection. Heat builds up within the connection due to the combination of high amperage current and a poor connection that increases the electrical resistance. The pin + socket connector (when connected) can be modeled as a simplified layered structure that contains a r₁=0.1mm copper layer (the pin), a 72 =1mm solder layer (the socket), and a 13 =1.5mm plastic cover layer. In reality the outside of the connector is not circular, but that is not important here. The thermal conductivities of these materials are estimated as Kcop=413W/mK, Ksol = 58W/mK, and Kplas = 0.2W/mK, respectively. Given the melting point of the plastic cover is 171°C, estimate the total power drawn (W) through the 6cm long connector at the time instant it starts to melt. Assume the following. The temperature is uniform in the copper pin layer at 217°C and the material properties are independent of temperature. The plastic melts all the way along the length of the pin. Total power can be estimated by Ptot = VI = Papu + Pheat, where Pgpu = 105W is the electric power transferred to the GPU through this connector, and Pheat refers to the electric power that is converted into heat due to the high electrical resistance of the poor connection.

Fig: 1