Inductor Circuit, separation of variables

In summary, we are given the equation V(t) = 2000e^(-100t) volts for t > 0 and values for initial currents i1(0) = -6A and i2(0) = 1A. From this, we can find the initial current i0(0) = 5A. We are then asked to find i0(t) for t > 0. After finding Leq = 4H, we use the equation V(t) = L di/dt and separate variables to integrate. However, the software is giving a different answer of 5e^(-.1t) possibly due to a change in units for "t".
  • #1
ElijahRockers
Gold Member
270
10

Homework Statement



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V_o varies as V(t) = 2000e^(-100t) volts for t > 0

i1(0) = -6A
i2(0) = 1A
thus
i0(0) = 5A

Find i0(t) for t > 0.

I found Leq = 4H

V(t) = L di/dt

I separated variables and integrated, got 5e^(-100t)

but the software is telling me it's wrong... supposedly the answer is 5e^(-.1t) and I'm not exactly sure how...

thanks

Homework Equations


The Attempt at a Solution

 
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  • #2
ElijahRockers said:

I separated variables and integrated, got 5e^(-100t)

but the software is telling me it's wrong... supposedly the answer is 5e^(-.1t) and I'm not exactly sure how...

They change the units of "t" to milliseconds. Their answer should have specified the units if not using SI.
 

1. What is an inductor circuit?

An inductor circuit is an electronic circuit that contains an inductor, which is a passive electronic component that stores energy in the form of a magnetic field. It is often used in conjunction with other components, such as resistors and capacitors, to create various electronic devices.

2. How does an inductor circuit work?

An inductor circuit works by storing energy in the form of a magnetic field when an electric current flows through it. When the current changes, the magnetic field also changes, which induces a voltage in the circuit. This voltage opposes the change in current, and thus the inductor acts as an energy storage device.

3. What is the separation of variables method?

The separation of variables method is a mathematical technique used to solve differential equations. It involves separating a multi-variable problem into several single-variable problems and solving each of them separately. It is often used in physics and engineering to solve problems involving inductor circuits.

4. Why is the separation of variables method useful in analyzing inductor circuits?

The separation of variables method is useful in analyzing inductor circuits because it allows us to break down complex differential equations into simpler parts, making the problem easier to solve. It also helps us understand the behavior of the inductor circuit in different situations and predict its performance.

5. What are some real-world applications of inductor circuits?

Inductor circuits have many real-world applications, including in power supplies, electric motors, generators, and electronic filters. They are also used in electronic devices such as radios, televisions, and computers to regulate current and voltage and filter out unwanted signals. Inductor circuits are also commonly found in medical equipment, automotive systems, and renewable energy technologies.

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