Find Inductor Value to Limit Current Increase in Circuit

[connor02]

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.

 

[spaceman231]

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)

 

[connor02]

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!

 

[NascentOxygen]

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.

 

[connor02]

Ah, I see, thank you NascentOxygen!