Stored Magnetic Energy - Inductor Circuit

In summary: Your method of integrating current and then multiplying by V is correct. Another way to approach it is to first find the power as a function of time, then integrate that to find the energy. Both methods are essentially the same, just using different "shortcuts" in the math. Good luck!In summary, we have a circuit consisting of a battery with an EMF of 12 V, a resistor with a resistance of 6.6 Ω, and an inductor with a long, thin cylindrical coil of wire with 30000 turns, a radius of 5 cm, and a length of 61 cm. After 1.4 seconds, the current through the battery is 0.8542201
  • #1
Bryon
99
0

Homework Statement


In the above circuit, the EMF from the battery is 12 V and the resistor has a resistance is 6.6 Ω. The inductor consists of a long, thin cylindrical coil of wire with 30000 turns, a radius of 5 cm and a length of 61 cm.

Answer the following questions for a time 1.4 seconds after the battery has been connected.

(c) How much energy has been delivered by the battery up to this point?


Homework Equations


U = 0.5LI^2

∫Udt from 0 to 1.4s

The Attempt at a Solution



I found the inductance and the current for the 1st two parts of the problem:

(a) What is the inductance of the solenoid? 14.56171141 H
(b) What is the current through the battery? 0.8542201 A

I plugged in the numbers to find the energy: U =0.5*14.56171141*(0.8542201^2) = 10.62556402 J

Then I think that you would have to integrate over time from 0 to 1.4s which gave me a result of 7.4378948 J.

It did not like the answer. Any suggestions?
 
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  • #2
you know the eqn of current in circuit at some time t

use it to find the charge flown through battery ... q = ∫i dt
where t changes from 0 to 1.4

now work done by battery = Q(EMF) = energy delivered
 
  • #3
Do I just inetrate (V/R)*(1-e^(Rt/L))? Its the only thing i can think of now that will be of any help. I tried to figure this one out from the hints you gave me but no luck.
 
  • #4
Bryon said:
Do I just inetrate (V/R)*(1-e^(Rt/L))? Its the only thing i can think of now that will be of any help. I tried to figure this one out from the hints you gave me but no luck.

You have the expression for the current with respect to time. That's the current that is being delivered by the battery to the circuit. Do you know what the instantaneous power (watts) delivered by the battery is?
 
  • #5
Yes, it is P=V*I(t). So, when I find the total current over time I can just plug it into that!
 
  • #6
Bryon said:
Yes, it is P=V*I(t). So, when I find the total current over time I can just plug it into that!

Yup. Integrate the power to find the total energy delivered.
 
  • #7
gneill said:
Yup. Integrate the power to find the total energy delivered.

But same is integrate current and then multiply by V

both methods seems different but are same, right?
 
  • #8
Thanks for the help! I see if i can get it in a bit!
 
  • #9
Yes; in this case the voltage is constant, so it can be "pulled out of" the integral.
 

1. What is a stored magnetic energy inductor circuit?

A stored magnetic energy inductor circuit is a type of electronic circuit that stores energy in the form of a magnetic field. It consists of an inductor, which is a coil of wire, and a power source, such as a battery or power supply. When a current flows through the inductor, a magnetic field is created, which stores energy. This energy can then be released when the current is switched off, creating a voltage spike in the circuit.

2. How does a stored magnetic energy inductor circuit work?

When a current flows through the inductor, a magnetic field is created around the coil. This magnetic field stores energy in the form of electromagnetic radiation. When the current is switched off, the energy stored in the magnetic field is released, causing a voltage spike in the circuit. This process is known as inductive kickback or back EMF (electromotive force).

3. What are the applications of a stored magnetic energy inductor circuit?

Stored magnetic energy inductor circuits are commonly used in electronic devices such as power supplies, motors, relays, and transformers. They are also used in circuits that require voltage spikes, such as ignition systems in cars and flash photography. Inductors are also used in filters to block certain frequencies of electrical signals.

4. What factors affect the amount of stored magnetic energy in an inductor circuit?

The amount of stored magnetic energy in an inductor circuit depends on the inductance of the coil, the current flowing through the coil, and the time it takes for the current to change. A larger inductance or higher current will result in more stored energy, while a shorter time for the current to change will result in less stored energy.

5. How can the stored magnetic energy in an inductor circuit be controlled?

The stored magnetic energy in an inductor circuit can be controlled by adjusting the inductance, the current, or the time it takes for the current to change. The inductance can be changed by using different types of inductor coils or by adding or removing turns from the coil. The current can be controlled by using a resistor in series with the inductor or by using a variable power supply. The time for the current to change can be controlled by using a capacitor in parallel with the inductor, which can slow down the rate of change of the current.

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