- #1
xconwing
- 20
- 0
How can you get from the first expression to the second. I've done calculus, just need a fresher. I don't know how to deal with the dt/dt
thanks
How to Simplify Inductor Expressions Using Calculus?
In summary, the conversation is about finding the second expression from the first expression and involves the use of calculus. The constant, L, is multiplied by the function i(t) and integrated with respect to time, resulting in (1/2)i^2(t) if the limit of i(t) as time approaches infinity is 0. However, if Li is a single function, this is not always true.
How can you get from the first expression to the second. I've done calculus, just need a fresher. I don't know how to deal with the dt/dt
thanks
- #2
HallsofIvy
Science Advisor
Homework Helper
- 42,988
- 981
What you have written is not clear. Is "Li" a single function or is this the constant, L, times the function i?
If the latter this is easy. [itex]L\int_{-\infty}^t i(\tau) (di/d\tau)d\tau= L\int_{-\infty}^t i di = L\left[(1/2)i^2(\tau)\right]_{\infty}^t[/itex] which, if [itex]\lim_{\tau\to\infty} i(\tau)= 0[/itex] is [itex](1/2)i^2(\tau)[/itex]
If Li is a single function, then it is NOT always true.
If the latter this is easy. [itex]L\int_{-\infty}^t i(\tau) (di/d\tau)d\tau= L\int_{-\infty}^t i di = L\left[(1/2)i^2(\tau)\right]_{\infty}^t[/itex] which, if [itex]\lim_{\tau\to\infty} i(\tau)= 0[/itex] is [itex](1/2)i^2(\tau)[/itex]
If Li is a single function, then it is NOT always true.
- #3
berkeman
Mentor
- 68,293
- 22,002
Yeah, L is the constant value of the inductance. i(t) is the current as a function of time.
FAQ: How to Simplify Inductor Expressions Using Calculus?
What is an inductor?
An inductor is an electrical component that stores energy in the form of a magnetic field. It is typically made of a coil of wire and is commonly used in electronic circuits.
How does an inductor work?
When an electric current flows through the coil of an inductor, it creates a magnetic field. This field then stores energy, which can be released when the current is turned off or changed. This property of an inductor is what allows it to resist changes in current.
What is the equation for calculating the power to work of an inductor?
The power to work of an inductor can be calculated using the equation P = (1/2) * L * I^2 * dI/dt, where P is power, L is inductance, I is current, and dI/dt is the rate of change of current over time.
How does the power to work of an inductor affect electronic circuits?
The power to work of an inductor is an important factor in electronic circuits as it can impact the efficiency and stability of the circuit. Inductors can also be used to regulate voltage and filter out unwanted signals.
Can the power to work of an inductor be increased or decreased?
Yes, the power to work of an inductor can be increased by increasing the current or inductance, or by decreasing the rate of change of current over time. It can be decreased by decreasing the current or inductance, or by increasing the rate of change of current over time.