First order circuits, Inductors

In summary: The resulting equation will be of the form i(t) = I + Ke^(-t/T). Remember that the current through the inductor must be continuous and the voltage across the inductor must be zero at t = 0+. In summary, the security alarm circuit for an office building door can be modeled using an inductor and a switch. When the switch is closed for a long time, the inductor is charged and at steady state. When the switch is opened, the circuit splits into two and the current through the inductor continues in the same direction. Using KVL, we can write the differential equation for the mesh and solve for the current i(t) with the initial condition i(0) = 2. The resulting
  • #1
popo902
60
0

Homework Statement


A security alarm for an office building door is modeled by the circuit [below]. The switch represents the door interlock, and v is the alarm indicator voltage. Find v(t) for t>0 for the circuit [below]. The switch has been closed for a long time at t=0-

http://i36.photobucket.com/albums/e47/jo860/img014.jpg

Homework Equations



V = L di/dt

The Attempt at a Solution



ok so, i see that it has been closed for a long time, which must mean the inductor is "charged" and at steady state at t=0-, t=0+, and i think also t=0 since current cannot change instantaneously
I used mesh analysis and found the current "stored" in the inductor to be 2A

then i see that when the switch is opened, it splits the circuit into two circuits...right?
so then only the left side is where i work.
then the inductor would sort of be like a finite current source pumping current through the 9 then 3 ohm resistor--the opposite way the previous current was going(is this correct?)

I see it like if i find the current through the inductor at t>0, then i just multiply that by 9 to get the voltage across 9
could someone maybe give me a hint to what I'm missing or if I'm wrong?
would it right to use KVL?
 
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  • #2
popo902 said:

Homework Statement


A security alarm for an office building door is modeled by the circuit [below]. The switch represents the door interlock, and v is the alarm indicator voltage. Find v(t) for t>0 for the circuit [below]. The switch has been closed for a long time at t=0-

http://i36.photobucket.com/albums/e47/jo860/img014.jpg

Homework Equations



V = L di/dt

The Attempt at a Solution



ok so, i see that it has been closed for a long time, which must mean the inductor is "charged" and at steady state at t=0-, t=0+, and i think also t=0 since current cannot change instantaneously
I used mesh analysis and found the current "stored" in the inductor to be 2A

then i see that when the switch is opened, it splits the circuit into two circuits...right?
so then only the left side is where i work.
then the inductor would sort of be like a finite current source pumping current through the 9 then 3 ohm resistor--the opposite way the previous current was going(is this correct?)
No, the current through the inductor continues in the same direction.
I see it like if i find the current through the inductor at t>0, then i just multiply that by 9 to get the voltage across 9
This is true only at t = 0. After that the current and consequently the voltage through the resistor will diminish.
could someone maybe give me a hint to what I'm missing or if I'm wrong?
would it right to use KVL?
You can use KVL to write the differential equation for the mesh. After that, you solve the equation with the initial condition i(0) = 2.
 

1. What is a first order circuit?

A first order circuit is a type of electrical circuit that contains only one energy storage element, such as a capacitor or an inductor. It is characterized by its ability to store and release energy, and its response to changes in voltage or current over time.

2. What is an inductor?

An inductor is an electrical component that stores energy in the form of a magnetic field. It is made up of a coil of wire, typically wrapped around a core material, and is used in circuits to block or allow the flow of alternating current.

3. How does an inductor work in a first order circuit?

In a first order circuit, an inductor resists changes in the flow of current by storing energy in its magnetic field. When a voltage is applied to the circuit, the inductor initially resists the flow of current, but as the magnetic field builds up, it allows current to flow more easily. When the voltage is removed, the inductor releases the stored energy, causing a brief surge of current in the opposite direction.

4. What are the applications of first order circuits and inductors?

First order circuits and inductors have a wide range of applications in electronics, including power supplies, filters, and oscillators. They are also commonly used in electric motors, generators, and transformers.

5. How do you calculate the voltage and current in a first order circuit with an inductor?

The voltage across an inductor in a first order circuit can be calculated using the formula V = L di/dt, where L is the inductance in henries and di/dt is the rate of change of current over time. The current in the circuit can be found by integrating the voltage over time using the equation i(t) = (1/L) ∫ V dt.

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