If iC=25 e^-40 t A, what is the time constant τand how long will the transient last?

Name: Problem 14, Chapter 11: Circuit Analysis - Theory and Practice
Uploaded: 2022-10-23T22:24:04-08:00
Duration: 2 min 22 s
Channel: Jacob Shpiece
Description: If iC=25 e^-40 t A, what is the time constant τand how long will the transient last?

step 1 The energy stored in a capacitor can be expressed as a function of the charge on the capacitor,

If iC=25 e^-40 t A, what is the time constant τand how long...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Exponential Decay in First-Order Systems

First-order systems exhibit an exponential decay behavior where the system variable (such as current or voltage) decreases according to an exponential function. The exponent's coefficient is related to the inverse of the time constant, governing how quickly the system reaches steady state.

Duration of Transient Response

The duration of a transient response in first-order systems is commonly approximated as lasting around 5 time constants. After this period, the transient effects become negligible, and the system is considered to have reached steady state.

Time Constant

In first-order circuits, the time constant (?) is a measure of the speed at which the transient response decays. It is defined as the product of resistance and capacitance in an RC circuit, or more generally the inverse of the coefficient in the exponent of an exponential response. A time constant indicates the time required for the response to decay to about 36.8% of its initial value.

Transcript

Please give Ace some feedback