Please answer all parts SHOWING ALL STEPS CLEARLY EXPLAINING THE CONCEPTS!! Also, please make sure all solutions are 100% correct. DO NOT USE CALCULUS (Integration, Cross product, etc.) TO SOLVE ANY OF THESE QUESTIONS. Thank you very much!

A 100 W lightbulb is designed to be connected to an AC voltage of 120 V (rms). What is the resistance (in () of the lightbulb filament at normal operating conditions? (1) 144 (2) 240 (3) 180 (4) 120 (5) 90Consider an oscillating LC circuit consisting of a capacitor with C = 1 mF, no resistance, and an unknown inductor L as shown in the gure. At a certain Q I moment of time the charge on the capacitor is 4 m0 and the current is 2 A. C If the maximum charge on the capacitor during the oscillations is 8 m0, what L is the inductance (in mH) of the unknown inductor L? (1) 12 (2) 5 (3) 32 (4) 28 (5) 40 In the previous problem, how much magnetic energy (in mJ) is in the inductor when the electric energy in the capacitor is 8 ml? (1) 24 (2) 12 (3) 54 (4) 6 (5) 8 Consider a resistor R and a capacitor C connected with an emf with oscillating voltage given by e(t) = (max sin(wt + () as shown in the figure. If R = 20, I(t) C = 0.01 F, Emax = 16 V, and w = 28.868 rad/s, what is the maximum current in the circuit (in A)? R E(t) C (1) 4 (2) 2 (3) 3 (4) 6 (5) 8 What is the average power dissipated in the resistor (in W) in the previous problem? (1) 16 (2) 4 (3) 9 (4) 8 (5) 32A massless and frictionless conducting rod is being rotated about one end at a constant angular speed (.0 along a semicircular conducting rail with radius r = 0.5 m by a constant external force Fext that is perpendicular to the rod. The xed end of the rotating rod is connected to the semicircular conducting rail through a 49 resistor forming a pie shaped circuit, as shown in the gure. The entire system is immersed in a uniform constant 2T magnetic eld (out of the paper). If (.0 = 16 rad/s, what is the induced current in the resistor (in A)? (1) 1.0 (2) 0.50 (3) 0.75 (4) 1.5 A square Wire loop with area A = 4.0 In2 rotates about the vertical yaxis at 3,600 rev/ min in a uniform magnetic eld that points in the xdirection, as shown in the gure. If the magnitude of the magnetic eld B = 20 mT, What is the maximum emf induced in the loop (in V)? 30.2 45.2 60.3 21.6 85.2 CHH>CADNJH