Solving Electrical Energy Dissipated in Wire Circuit

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SUMMARY

The discussion focuses on calculating the average electrical energy dissipated in a copper wire formed into a circular loop with a radius of 9 cm, subjected to a magnetic field increasing from 0 to 0.70 T over 0.45 seconds. The resistance per unit length of the wire is 3.3 x 10^-2 Ω/m. Key calculations include an electromotive force (emf) of -80.15 V, a resistance of 0.01866 Ω, and an incorrect power calculation resulting in -344264.29 W. The participants emphasize the importance of maintaining unit consistency throughout calculations to avoid errors.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Knowledge of Ohm's Law and electrical resistance calculations
  • Familiarity with magnetic flux and its relationship to magnetic fields
  • Ability to perform unit conversions and dimensional analysis
NEXT STEPS
  • Review Faraday's Law and its application in calculating emf
  • Learn about calculating resistance in circular wire loops
  • Study the relationship between magnetic flux and magnetic field strength
  • Explore techniques for error checking in electrical calculations
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and anyone involved in electromagnetic theory and circuit analysis, particularly those working with inductive components and energy dissipation in circuits.

tj03
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I have worked my way through this question, and I still get a wronge answer.

A piece of copper wire is formed into a single circular loop of radius 9 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.
r= 9cm= .09m
change in t= .45s
B= .70T
restitance per unit length= 3.3 x 10^-2
N= 1
emf=-80.15
mag flux 178.12

I figured R to = .01866
I = 4295.25
P= -344264.29 (I *EMF)
E= 344264.633 (pt)

anyone know where I went wrong?
 
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Couple suggestions -- First, carry units through in all your calculations. It will help you to avoid mistakes, and will help us to read your calcs a lot easier (at least for me). Second, the power will not be negative, and it woun't be 3244264 in any reasonable units. You also probably won't get an emf of 80V with a single turn and that slow ramp rate.

Show us which equations you are trying to use, and show all your units so we can help you if you still don't get it.
 
How did you calculate the emf?

What is the relationship between emf and the changing rate of the magnetic flux, and the magnetic flux and magnetic field strength?
 

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