Inductor Voltage Maximum and Maximum Voltage Calculation

In summary, the voltage across the inductor is maximum at t = 0.0027679s with a value of 1000000*e^-200(0.0027679)(2cos400(0.0027679)-sin400(0.0027679)) = 21.848V.
  • #1
Zarathuztra
36
0

Homework Statement


The current in a 25mH inductor is known to be - 10A for t <= 0 and (-10cos400t - 5sin400t)e^-200t A for t >= 0. Assume the passive sign convention.

Part A: At what instant of time is the voltage across the inductor maximum?
Part B: What is the maximum voltage?

Homework Equations


V=L*di/dt


The Attempt at a Solution



I took the derivative of (-10cos400t - 5sin400t)e^-200t, then took the derivative again, set to zero, and found the value of t at that point.

5000*e^(-200t)*sin(400t)

1000000*e^(-200t)(2cos400t - sin400t) = 0 @ t = 0.01339 s

Where am I going wrong? Am I missing something?
 
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  • #2
t = 0.01339 s doesn't look like a zero of that function to me...
 
  • #3
your right, that's way off... looking at it again.

I need 2cos400t - sin400t to equal 0...

2cosx = sinx
2 = tanx
arctan(2) = x

x = 1.107s

this didn't work.. is my derivative correct? I'm pretty sure my algebra and trig were correct.
 
Last edited:
  • #4
Zarathuztra said:
your right, that's way off... looking at it again.

I need 2cos400t - sin400t to equal 0...

2cosx = sinx
2 = tanx
arctan(2) = x

x = 1.107s

this didn't work.. is my derivative correct? I'm pretty sure my algebra and trig were correct.

You've solved for the angle, x. But the angle is not t...
 
  • #5
hahaha, what a silly mistake, I used a variable in place of 400t and didn't sub the variable out... x/400 = t so, 1.107/400 = t = .0027679s
 
  • #6
Yes, that looks much better :smile:
 

1. What is an inductor in a first order circuit?

An inductor is a passive electrical component that stores energy in the form of a magnetic field. It is represented by the symbol L and has the unit of henry (H). In first order circuits, inductors are often used to smooth out voltage variations and to filter out high-frequency noise.

2. How does an inductor behave in a first order circuit?

In a first order circuit, the behavior of an inductor can be described by the following equation: V = L di/dt. This means that the voltage across an inductor is proportional to the rate of change of current flowing through it. Therefore, inductors oppose changes in current and act as a low-pass filter.

3. What is the time constant of an inductor in a first order circuit?

The time constant of an inductor in a first order circuit is given by the formula τ = L/R, where L is the inductance in henrys and R is the resistance in ohms. This represents the amount of time it takes for the current in the circuit to reach 63.2% of its final value when a constant voltage is applied.

4. How do you calculate the energy stored in an inductor?

The energy stored in an inductor can be calculated using the formula E = 1/2 * L * I^2, where L is the inductance in henrys and I is the current in amperes. This formula shows that the energy stored in an inductor is directly proportional to its inductance and the square of the current flowing through it.

5. What is the behavior of an inductor when there is a sudden change in voltage?

When there is a sudden change in voltage in a first order circuit, the inductor will try to maintain the current flowing through it. This means that a sudden increase in voltage will cause the inductor to oppose the change by generating a back EMF, while a sudden decrease in voltage will cause the inductor to maintain the current by acting as a voltage source.

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