Current and Resistance

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Define the current.

Understand the microscopic description of

current.

Discuss the rat at which the power transfer to a

device in an electric current.

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2-1 Electric current

2-2 Resistance and Ohm’s Law

2-3 Current density, conductivity and

resistivity

2-4 Electrical Energy and Power

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Whenever electric charges of like signs move, an

electric current is said to exist.

The current is the rate at which the charge flows

through this surface

◦ Look at the charges flowing perpendicularly to a surface of

area A

The SI unit of current is

Ampere (A) 1 A = 1 C/s

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QI

t

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∆Q is the amount of charge that

passes through this area in a

time interval ∆ t,

the average current Iav is equal to the

charge that passes through “A” per

unit time

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We define the instantaneous current I as

the differential limit of average current:

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The direction of the current is the direction

positive charge would flow

◦ This is known as conventional current direction

In a common conductor, such as copper, the current is

due to the motion of the negatively charged electrons

It is common to refer to a moving charge as a mobile

charge carrier . A charge carrier can be positive or

negative. For example, the mobile charge carriers in a

metal are electrons.

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Charged particles move

through a conductor of cross-

sectional area A

n is the number of charge

carriers per unit volume

n A Δx is the total number of

charge carriers

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The total charge is the number of carriers times the charge

per carrier, q

◦ ΔQ = (n A Δx) q

The drift speed, vd, is the speed at which the carriers move

◦ vd = Δx/ Δt

Rewritten: ΔQ = (n A vd Δt) q

Finally, current, I = ΔQ/Δt = nqvdA

OR

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the average current in the conductor

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If the conductor is isolated, the electrons undergo

random motion

When an electric field is set up in the conductor, it

creates an electric force on the electrons and

hence a current

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The zig-zag black line represents the motion of charge carrier in a conductor The net drift speed is small

The sharp changes in direction are due to collisions

The net motion of electrons is opposite the direction of the electric field

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Consider a conductor of cross-sectional area

A carrying a current I. The current density J in

the conductor is defined as the current per unit

area. Because the current I = nqvdA,

the current density is:

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the current density is proportional to the electric field:

Where σ the constant of

proportionality & is called the

conductivity of the conductor.

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If the field is assumed to be uniform,

the potential difference is related to

the field through the relationship

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express the magnitude of the current

density in the wire as

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Where ,J = I/A, we can write the potential

difference as

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The quantity R = ℓ/σA is called the resistance of

the conductor. We can define the resistance as

the ratio of the potential difference across a

conductor to the current in the conductor:

,

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1. Material property—each material will oppose the flow of

current differently.

2. Length—the longer the length , the more is the

probability of collisions and, hence, the larger the

resistance.

3. Cross-sectional area—the larger the area A, the easier

it becomes for electrons to flow and, hence, the lower the

resistance.

4. Temperature—typically, for metals, as temperature

increases, the resistance increases

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Thus, the resistance R of any material with a uniform cross-

sectional area A and length (as shown in Fig) is directly

proportional to the length and inversely proportional to its

cross-sectional area. In mathematical form,

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In a conductor, the voltage applied across the

ends of the conductor is proportional to the current

through the conductor

The constant of proportionality is the resistance of

the conductor

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VR

I

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Units of resistance are ohms (Ω)

◦ 1 Ω = 1 V / A

Resistance in a circuit arises due to collisions

between the electrons carrying the current with

the fixed atoms inside the conductor

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Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents

This statement has become known as Ohm’s Law

◦ ΔV = I R

Ohm’s Law is an empirical relationship that is valid only for certain materials ◦ Materials that obey Ohm’s Law are said to be Ohmic

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An ohmic device

The resistance is

constant over a wide

range of voltages

The relationship

between current and

voltage is linear

The slope is related to

the resistance

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Non-Ohmic materials are

those whose resistance

changes with voltage or

current

The current-voltage

relationship is nonlinear

A diode is a common

example of a non-Ohmic

device

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The electric current I in a conductor is defined as

The average current in a conductor is related to the motion of

the charge carriers through the relationship

The magnitude of the current density J in a conductor is the

current per unit area:

The current density in an ohmic conductor is proportional to

the electric field according to the expression

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The resistance R of a conductor is defined as

where ∆V is the potential difference across it, and I is

the current it carries.

For a uniform block of material of cross sectional area

A and length L, the resistance over the length L is

where ρ is the resistivity of the material.

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