Find Inductor Value to Limit Current Increase in Circuit

In summary, the question asks for the value of inductor to be added to a circuit with a resistance of 175Ω and an ideal battery with an emf of 6.3V in order to ensure that the current increase in the first 58μs is less than 4.9mA. The correct equation to use is I=Io(1-e^(-Rt/L)) and solving for L gives a value of 0.069H. The incorrect approach used an assumption of circuit resistance = 0 and all 6.3V applied across the inductor, leading to a wrong answer.
  • #1
connor02
27
0

Homework Statement



Your circuit has a resistance of 175Ω and an ideal battery with an emf of 6.3V. What value of inductor should you add to the circuit to ensure the current increase in the first 58μs is less than 4.9mA?

Homework Equations



I think

E=L(di/dt)


The Attempt at a Solution



E=L(di/dt)

6.3=L(4.9*10^-3/58*10^-6)

L = 0.07457H

But the answer is 0.069H

Thanks.
 
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  • #2
I believe you want to use the equation for current growth through a inductor. Also di/dt doesn't equal (4.9*10^-3/58*10^-6)
 
Last edited:
  • #3
WOW you're right! Thanks!

Then the formula would be I=Io(1-e^(-Rt/L))

Io=6.3/175=0.036A

Solving for L, L=0.069H.

But why is my method wrong? and why is di/dt not (4.9*10^-3/58*10^-6)? di is 4.9*10^-3 and dt is 58*10^-6 right?

Thank you!
 
  • #4
When current is flowing, KVL says that the 6.3V is shared (unevenly) between the resistance and the inductance. Your "approach" assumes circuit resistance = 0 and all 6.3V is applied across the inductor.
 
  • #5
Ah, I see, thank you NascentOxygen!
 

What is an inductor?

An inductor is an electronic component that is designed to store energy in the form of a magnetic field. It is typically made of a coiled wire and is used in circuits to control the flow of current.

Why is it important to limit current increase in a circuit?

Limiting current increase in a circuit is important for several reasons. It can help prevent damage to components, ensure that the circuit operates within its designed parameters, and improve the overall safety of the circuit.

How does an inductor help limit current increase in a circuit?

An inductor helps limit current increase in a circuit by resisting changes in the flow of current. When the current in a circuit increases, the inductor produces a counter electromotive force (EMF) that opposes the current, thus limiting its increase.

How do I calculate the value of an inductor to limit current increase in a circuit?

To calculate the value of an inductor to limit current increase in a circuit, you will need to know the desired maximum current and the frequency of the circuit. You can then use the formula L = V/(2πfI) to determine the inductance value in Henrys (H).

What are some factors that can affect the effectiveness of an inductor in limiting current increase?

The effectiveness of an inductor in limiting current increase can be affected by factors such as the quality and type of the inductor, the frequency of the circuit, and the materials and design of the circuit. Other external factors like temperature and magnetic interference can also impact the inductor's performance.

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