- #1
Nicole D
- 3
- 1
Homework Statement
L = 20mH = 20 x 10-3 H
i = 40 mA for t≤0
i = A1e-10,000t + A2e-40,000t A for t≥0
The voltage at t=0 is 28 V.
I have to find the equation for the voltage for t>0.
Then I have to find the time when power is zero.
Homework Equations
v(t) = L* di/dt
p(t) = L*i* di/dt
The Attempt at a Solution
I know that current through an inductor has to be continuous, so at t=0, I can say:
A1 + A2 = 40 x 10-3 A
I then found di/dt:
di/dt = -10,000A1e-10,000t - 40,000A2e-40,000t
Since v = L di/dt:
v = (20 x 10-3 H)*(-10,000A1e-10,000t - 40,000A2e-40,000t)
v = -200A1e-10,000t - 800A2e-40,000t
At t=0, v=28 V, so:
v(t=0) = -200A1 - 800A2 = 28 V
So I have the following two equations:
A1 + A2 = 40 x 10-3 A
-200A1 - 800A2 = 28 V
When I solve these using matrices on my calculator, I get:
A1 = 0.1
A2 = -0.06
When I plug those into the equation for v, I get:
v(t) = -20A1e-10,000t + 48A2e-40,000t
This answer is one of the multiple choice answers. However, the system tells me this answer is wrong and the correct answer is:
v(t) = 18A1e-10,000t + 10A2e-40,000t
I don't understand why my answer is wrong, so any explanation would be appreciated!
Once I understand that, I know that to find the time when power is zero, I just set p(t) = L*i* di/dt to zero and solve for t.