# 9.1 Electrical current

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By the end of this section, you will be able to:
• Describe an electrical current
• Define the unit of electrical current
• Explain the direction of current flow

Up to now, we have considered primarily static charges. When charges did move, they were accelerated in response to an electrical field created by a voltage difference. The charges lost potential energy and gained kinetic energy as they traveled through a potential difference where the electrical field did work on the charge.

Although charges do not require a material to flow through, the majority of this chapter deals with understanding the movement of charges through a material. The rate at which the charges flow past a location—that is, the amount of charge per unit time—is known as the electrical current . When charges flow through a medium, the current depends on the voltage applied, the material through which the charges flow, and the state of the material. Of particular interest is the motion of charges in a conducting wire. In previous chapters, charges were accelerated due to the force provided by an electrical field, losing potential energy and gaining kinetic energy. In this chapter, we discuss the situation of the force provided by an electrical field in a conductor, where charges lose kinetic energy to the material reaching a constant velocity, known as the “ drift velocity .” This is analogous to an object falling through the atmosphere and losing kinetic energy to the air, reaching a constant terminal velocity.

If you have ever taken a course in first aid or safety, you may have heard that in the event of electric shock, it is the current, not the voltage, which is the important factor on the severity of the shock and the amount of damage to the human body. Current is measured in units called amperes; you may have noticed that circuit breakers in your home and fuses in your car are rated in amps (or amperes). But what is the ampere and what does it measure?

## Defining current and the ampere

Electrical current is defined to be the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large amount of charge moves through the wire in a small amount of time. If the current is small, such as that used to operate a handheld calculator, a small amount of charge moves through the circuit over a long period of time.

## Electrical current

The average electrical current I is the rate at which charge flows,

${I}_{\text{ave}}=\frac{\text{Δ}Q}{\text{Δ}t},$

where $\text{Δ}Q$ is the amount of charge passing through a given area in time $\text{Δ}t$ ( [link] ). The SI unit for current is the ampere (A), named for the French physicist André-Marie Ampère (1775–1836). Since $I=\frac{\text{Δ}Q}{\text{Δ}t}$ , we see that an ampere is defined as one coulomb of charge passing through a given area per second:

$1\text{A}\equiv 1\frac{\text{C}}{\text{s}}.$

The instantaneous electrical current, or simply the electrical current    , is the time derivative of the charge that flows and is found by taking the limit of the average electrical current as $\text{Δ}t\to 0$ :

$I=\underset{\text{Δ}t\to 0}{\text{lim}}\frac{\text{Δ}Q}{\text{Δ}t}=\frac{dQ}{dt}.$

Most electrical appliances are rated in amperes (or amps) required for proper operation, as are fuses and circuit breakers.

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