Inductance and RL circuits help

[christianerik]

If the switch is closed at t = 0, find the
current in the inductor at t = 0.224 s. Answer
in units of A.
&
Find the current in the switch at that same
time.

I know that i must use i = V/R(1 - e^-t/L/R) but can't seem to get the right answer.

Any help is appreciated...5 ohms
-------------^^^^^^^------I
I.......I
I...10 ohms...1.4 H...I
I------^^^^^^^^---&&&&--I
I.......I
I...S...30 V...5 ohms.I
I-------/..---I I----^^^^^--I

Homework Statement

What am I doing wrong?

Homework Equations

i = V/R(1 - e^-t/L/R)

The Attempt at a Solution

i = V/R(1 - e^-t/L/R + V/5 = (30 - V)/5

(V/10)( 1 - e^-(0.224*10/1.4) + V/5 = -V/5 + 6

0.1V(0.798)+0.4V = 6

(0.4+0.0798)V = 6

V = 6/0.4798 = 12.5 v

The inductor current at t = 0.224 s

i = V/R(1 - e^-t/L/R)

i = (12.5/10)[ 1 - e^-(0.224(10/1.4) ]

i = 0.9976 A

The switch current:

Is = i + V/5 = 0.9976 + 12.5/5 = 3.497 A

 

[rl.bhat]

First of all you have to find the voltage across LR circuit.
At t=0 L acts like a conductor. Find the total resistance and current in the circuit. Hence find the voltage across LR circuit.Then use relevant formula to find the current in L.

 

[kerimek]

It seems like you have the right approach, but your calculations may be a bit off. First, let's look at the equation you are using:

i = V/R(1 - e^-t/L/R)

This equation assumes that the switch is closed at t=0, so there is no need to add V/5 to the equation. Also, the equation should be:

i = V/R(1 - e^-t/R/L)

Notice that the order of R and L are switched compared to what you wrote. This is important because the time constant for an RL circuit is L/R, not R/L. So let's rewrite the equation using the correct order:

i = V/R(1 - e^-t/R/L)

Now let's plug in the values given in the problem:

i = (30/10)(1 - e^-(0.224/5))

i = 3(1 - e^-0.0448)

i = 3(1 - 0.955)

i = 3(0.045)

i = 0.135 A

So the current in the inductor at t = 0.224 s is 0.135 A.

To find the current in the switch, we simply add V/R to the equation:

Is = i + V/R = 0.135 + 30/10 = 3.135 A

So the current in the switch at t = 0.224 s is 3.135 A.