Solved: The purpose of this problem is to show that the

Chapter 22, Problem 22.135

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The purpose of this problem is to show that the work W needed to establish a final current If in an inductor is (Equation 22.10). In Section 22.8 we saw that the amount of work needed to change the current through an inductor by an amount is where L is the inductance. The drawing shows a graph of LI versus I. Notice that is the area of the shaded vertical rectangle whose height is LI and whose width is Use this fact to show that the total work W needed to establish a current If is 81. A solenoid has a cross-sectional area of 6.0 104 m2 , consists of 400 turns per meter, and carries a current of 0.40 A. A 10-turn coil is wrapped tightly around the circumference of the solenoid. The ends of the coil are connected to a 1.5- resistor. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time of 0.050 s. Find the average current induced in the coil. 82. A 60.0-Hz generator delivers an average power of 75 W to a single light bulb. When an induced current exists in the rotating coil of a generator, a torquecalled a countertorqueis exerted on the coil. Determine the maximum countertorque in the generator coil. (Hint: The peak current, peak emf, and maximum countertorque all occur at the same instant.) Current, I If LI LIf I W 1 2LI 2 f .