What is the electrical energy dissipated in the resistor in 37.0 s? A 1000-turn

Question

What is the electrical energy dissipated in the resistor in 37.0 s?

A 1000-turn loop (radius = 0.036 m of wire is connected to a 25.0 ohm resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the loop. The field points into the paper and has a magnitude that varies in time as B = gt, where g = 0.25 Tesla per second. Neglect the resistance of the wire. What is the magnitude of the potential difference between points a and b? 1.018 V What is the electrical energy dissipated in the resistor in 37.0 s?

Explanation / Answer

magnetic flux through loop = N B A

induced emf = rate of change of magnetic flux

= d(NBA)/dt = N A dB/dt

= N A g

= 1000 x (pi x 0.036^2) x 0.25

= 1.02 Volt .....Ans

rate of energy dissipated = V^2 / R = 1.02^2 / 25

= 0.0414 W

energy = rate x time

= 0.0414 x 37

= 1.53 J .......Ans

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