Calculating Energy Transfer in an Inductor Circuit

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SUMMARY

The discussion focuses on calculating energy transfer in an inductor circuit with a coil of inductance 2.0 H and resistance 10 ohms connected to a 100 V ideal battery. At 0.10 seconds after connection, the energy stored in the magnetic field is 240 J, thermal energy in the resistance is 150 J, and energy delivered by the battery is 390 J. The current in the circuit is determined using the equation I = Io(1 - e^(-t/τ)), where Io is the steady-state current E/R.

PREREQUISITES
  • Understanding of inductance and resistance in electrical circuits
  • Familiarity with the formula for energy stored in an inductor: UL = 0.5LI²
  • Knowledge of the relationship between voltage, current, and resistance (Ohm's Law)
  • Basic understanding of exponential functions and time constants in RL circuits
NEXT STEPS
  • Study the derivation and application of the time constant τ in RL circuits
  • Learn how to calculate energy transfer rates in inductive circuits
  • Explore the implications of the equation I = Io(1 - e^(-t/τ)) in circuit analysis
  • Investigate the effects of varying resistance and inductance on energy transfer
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding energy dynamics in inductive circuits.

dwn
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Homework Statement



A coil with an inductance of 2.0 H and a resistance of 10 ohm is suddenly connected to an ideal battery with E = 100 V. At 0.10 s after the connection is made, what is the rate at which:

(a) energy is being stored in the magnetic field, ans: 2.4*102
(b) thermal energy is appearing in the resistance, and ans: 1.5*102
(c) energy is being delivered by the battery? ans: 3.9*102

Homework Equations



UL=.5LI2
VR=E(1-e-t/tau)

The Attempt at a Solution



V=IR 100/10 = I = 10 A
UL= .5*2*102 = 100

Clearly I'm missing a step or another equation to derive the current because I don't believe 10 A is correct. Please advise!
 
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10 A is the current after infinite time, and it is equal to Io= E/R. (E is the emf of the battery)

The current changes according to the function I=Io(1-e-t/τ).

You need to calculate the rate of changes of energies at t= 10 s.

ehild
 

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