Calculating Energy Transfer in an Inductor Circuit

In summary, a coil with an inductance of 2.0 H and a resistance of 10 ohm is connected to a battery with an emf of 100 V. At 0.10 s after the connection, the rate at which energy is being stored in the magnetic field is 2.4*102, the rate at which thermal energy is appearing in the resistance is 1.5*102, and the rate at which energy is being delivered by the battery is 3.9*102. To calculate the current at 0.10 s, the equation I=Io(1-e-t/τ) should be used.
  • #1
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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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  • #2
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
 

Related to Calculating Energy Transfer in an Inductor Circuit

1. What is an inductor and how does it work?

An inductor is a passive electronic component that is designed to store energy in the form of a magnetic field. It typically consists of a coil of wire that is wound around a core material, such as iron, which helps to increase the strength of the magnetic field. When current flows through an inductor, the magnetic field is created and energy is stored in the form of this field. When the current stops, the magnetic field collapses and releases this stored energy.

2. What is the role of inductors in electronic circuits?

Inductors play a vital role in electronic circuits, especially in circuits where the flow of electricity needs to be controlled. They are commonly used in filters, oscillators, and power supplies to regulate and smooth out the flow of current. They are also used in combination with capacitors to create resonant circuits, which are used in applications such as radio broadcasting and wireless communication.

3. How are inductors measured and what are the units of measurement?

Inductors are typically measured using a device called an inductance meter or an LCR meter. The unit of measurement for inductance is the henry (H), which is equivalent to 1 volt-second per ampere. Inductors can also be measured using an oscilloscope and a function generator by observing the voltage across the inductor as the frequency of the input signal is varied.

4. What factors affect the inductance of an inductor?

The inductance of an inductor is affected by several factors, including the number of turns in the coil, the shape and size of the coil, the type of core material used, and the presence of nearby conductors. The inductance can also be varied by changing the physical properties of the inductor, such as its length, cross-sectional area, and the spacing between the turns of the coil.

5. How do inductors interact with other components in a circuit?

Inductors interact with other components in a circuit in various ways. In series circuits, inductors can act as a resistance to the flow of current, while in parallel circuits they can act as a short circuit. They can also interact with capacitors to create resonant circuits, as mentioned previously. Additionally, inductors can generate electromagnetic interference (EMI) and can be used in circuits to filter out unwanted EMI.

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