Electrical energy dissipated in resistance of a wire

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SUMMARY

The discussion centers on calculating the average electrical energy dissipated in a copper wire formed into a circular loop with a radius of 10 cm, subjected to a changing magnetic field. The user applied the equations for electromotive force (Emf = -NAB/t), power (P = V^2/R), and energy (E = Pt) but arrived at an incorrect energy value of 0.052 J. The user calculated the resistance using the wire's resistance per unit length of 3.3 x 10^-2 /m and the circumference of the loop, but the final energy calculation was incorrect due to a miscalculation in power or resistance.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Knowledge of electrical resistance and Ohm's Law
  • Familiarity with power calculations in electrical circuits
  • Basic grasp of energy dissipation in resistive components
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  • Review the derivation and application of Faraday's Law in electromagnetic systems
  • Study the relationship between resistance, voltage, and power in electrical circuits
  • Learn about calculating energy dissipation in resistive materials
  • Explore advanced topics in electromagnetic induction and energy conversion
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Students studying electromagnetism, electrical engineers, and anyone involved in physics or electrical circuit design who seeks to understand energy dissipation in conductive materials.

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Homework Statement



A piece of copper wire is formed into a single circular loop of radius 10 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.70 T in a time of 0.45 s. The wire has a resistance per unit length of 3.3 10-2 /m. What is the average electrical energy dissipated in the resistance of the wire.

Homework Equations



Emf = -NAB/t
P = V(^2)/R
E = Pt

The Attempt at a Solution



I used The first equation to find emf... -.0489V
with that I plugged it into the second equation (for R I took my resistance per unit length times the circumference of my circle - pi*d)
so for my power I got .0489^2/.0207 = .1155
Then I thought I would just plug that number into the third equation
E = .1155w(.45s)
which would give me .052 J
but this isn't the right answer.
Where did I go wrong?
 
Physics news on Phys.org
The method and numbers look okay to me.
 

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