Finding i(t) (Source Free RL Circuit)

In summary, the conversation is about finding the equation for a source-free RL circuit. The equation is i(t) = i(0)e^(-t)/T, where T = L/Req. In this case, i(0) is found to be 5mA, and Req is calculated to be 3/4k Ohms. The switch is closed for a very long time (t<0) and then opened at t=0. The equation is confirmed by all parties involved.
  • #1
salman213
302
1
1. http://img529.imageshack.us/img529/6205/87421877rv5.jpg [/URL]3. First I found i(0)

the equation for a source free RL circuit is

i(t) = i(0)e^(-t)/T

T = L/ReqSince the inductor will be shorted when t<0, i(0) must be 5mA.

Now to find Req I added series and parallel appropriately to find

Req = 3/4k Ohms

so my equation is

i(t)= (5x10^-3)e^(-t)/T
where T = (1x10^-3)/(3/4x10^3)can someone please check that, Thanks!
 
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  • #2
By that arrow pointing to t=0, do you mean that the switch is closed for a very long time for t<0 and is opened at t=0?
 
  • #3
ya for a very long time (t<0) the switch is "horizontal" then at t=0 it is moved to the lower point.
 
  • #4
Yeah I got the same answer.
 
  • #5
ok great, thanks!
 

FAQ: Finding i(t) (Source Free RL Circuit)

1. What is a source free RL circuit?

A source free RL circuit is a circuit that does not have a voltage or current source connected to it. This means that there is no external power supply influencing the behavior of the circuit.

2. How do you find i(t) in a source free RL circuit?

To find i(t) in a source free RL circuit, you can use Kirchhoff's voltage law (KVL) and the differential equation for an RL circuit. KVL states that the sum of all voltage drops in a closed loop must equal the sum of all voltage rises, which can be used to solve for i(t) in the differential equation.

3. What is the differential equation for an RL circuit?

The differential equation for an RL circuit is: L(di/dt) + Ri = V, where L is the inductance in henries, R is the resistance in ohms, i is the current in amps, t is time in seconds, and V is the voltage in volts.

4. Can you solve for i(t) analytically in a source free RL circuit?

Yes, you can solve for i(t) analytically in a source free RL circuit by using the differential equation and applying integration. However, the process can be complex and may require advanced mathematical skills.

5. Are there any other methods for finding i(t) in a source free RL circuit?

Yes, there are other methods for finding i(t) in a source free RL circuit, such as using Laplace transforms or using a circuit simulator program. These methods may be more efficient and accurate, especially for more complex circuits.

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