Steady State

claimed by Shirin Kale

Steady state is the term used to describe an assembled circuit in which the current is constant and stays approximately constant for a very long time.

The Main Idea

After a circuit has been assembled, it can be described as steady state if it meets the following requirements:

-mobile charges are moving with constant drift velocity anywhere in the circuit

-no excess charges accumulate anywhere in the circuit

Although mobile charges are moving, the drift velocities of the charges do not vary with time at any location in the circuit and thus, the current is constant throughout the circuit. However, since current is also a function of the cross-sectional area and charge density (composition) of the wire - as shown by the equation for conventional current below:

I = |q|nAv

a steady state circuit is more specifically described as one in which the current is constant in each section of a wire with uniform thickness and composition.

[IMAGE]

The circuit above is an example of a circuit in the steady state.

Because mobile charges are moving in the circuit, there must be an applied electric field inside the wire that causes the mobile charges to move. And since there is no excess charge inside the wire, the electric field must be produced from surface charges. And because this electric field is responsible for moving the mobile charges inside the wire, the direction of the electric field at each location in the wire must be parallel to the wire.

Once a circuit is described as being in the steady state, there are three things we know to be true. It is true that: -there must be an E field in the wire -the E field has uniform magnitude throughout the wire -the E field is parallel to the wire at every location along the wire

When you assume that a circuit is in steady state, you are basically assuming that the circuit has been assembled and connected for a long time (such that the current is constant). However, there is a process that occurs - when the circuit is first assembled - before the circuit reaches steady state.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

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Examples

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