Calculate DC current through an inductor?

  • Thread starter hobbs125
  • Start date
  • #1
108
0
Hi everyone,

Say I have a series DC circuit. The circuit contains a 100V DC source, a switch, a 1.5H inductor, and a 1nF capacitor (all in series).

If I close the switch for 2uS what is the current at that time?

Initially I thought I could rearrange V=L*di/dt to

V*Ton/L = di/dt which would be 100*.000002/.150=1.3mA???

For some reason I am thinking this is not right since the capacitor charge should also effect the current.

Can anyone help me understand and calculate this correctly?
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
Once you have turned the circuit on it settles to a steady state very quickly - so you use V=IR - where R is the DC resistance of the inductor. An ideal inductor is just a length of wire ... R=0.

The transient response requires you solve the differential equation.

For an ideal switch closed for time T, ##v(t)=V_0\big ( u(t)-u(t-T)\big )##
 
  • #3
72
11
Include the cap voltage too, which is 1/c times integral of i(t) dt. Basically a KVL. Take derivative to get rid of integral and get a 2nd order diff eq. Then solve for i(t)
 
  • #4
108
0
Ok, I guess I need to go study differential equations. Never got that far in math.

Could anyone show me step by step how to solve?
 
Last edited:
  • #5
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
I missed the cap - right ... the solution is a damped/driven harmonic oscilator.
You can look it up. The driving function is the unput voltage as a function of time.
The u(t) function in post #2 are the Heaviside step function ... which you can look up too.

It would be a bit like pushing a pendulum off equilibrium and holding it for a bit before letting it go.

What you get is, basically, called the "impulse response" of the RCL circuit.
That's something else you can look up.

If you set it up right you can make it "ring" like a bell.
 

Related Threads on Calculate DC current through an inductor?

  • Last Post
Replies
4
Views
1K
Replies
12
Views
5K
Replies
8
Views
12K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
21
Views
3K
Replies
7
Views
400
Replies
7
Views
2K
Replies
5
Views
1K
Replies
6
Views
10K
Replies
6
Views
2K
Top