Derive equations for magnitude and phase of current and voltages on resistor and inductor in the phasor domain. assume that the resistance of the resistor is r, inductance of the inductor is l, magnitude of the source voltage is vm and phase of the source voltage is θ. note that you don’t have numbers in this step, so to find the magnitude and phase for current i and voltages vr and vl you must first derive both numerator and denominator in polar form using variables r, omega, l, vm, vphase (do not use numbers). the solutions should look like equations in slide 24/27!

Asteel tube (k=50 w/mk) of inner and outer diameter di = 20mm and do=26mm, respectively, is used to transfer heat from hot gases flowing over the tube (h-hot = 200w/m2k) to cold water flowing through the tube (h-cold = 8000 w/m2k). what is the cold-side overall heat transfer coefficient uc? to enhance heat transfer 16 straight fins of rectangular profile are installed longitudinally along the outer surface of the tube. the fins are equally spaced around the circumference of the tube, each having a thickness of 2mm and a length of 15mm. what is the corresponding overall heat transfer coefficient uc? *solve for uc in both cases*