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### Chapter 27

Current and Resistance

Intro

- Up until now, our study of electricity has been focused Electrostatics (charges at equilibrium conditions).
- We will now look at non-equilibrium conditions, and we will define electric current as the rate of flow of charge.
- We will look at current at the microscopic levels and investigate factors oppose current as well.

27.1 Electric Current

- Current- any net flow of charge through some region.
- A similar analogy would be water current, or the volume of water flowing past a given point per unit time (shower heads, rivers etc.)

- The rate of charge passing
perpendicularly through a

given area.

27.1

- The average current
- The instantaneous current
- The SI unit of current is the Ampere (A)

27.1

- Current Direction-
- Traditional- in the direction the flow of positive charge carriers.
- Conducting Circuits- Electrons are the flowing charge, current is in the opposite direction of the flow of negative charge carriers (electrons).
- Particle Accelerator- with the beam of positive charges
- Gases and Electrolytes- the result of both positive and negative flowing charge carriers.

27.1

- At the microscopic level we can relate the current, to the motion of the charge carriers.
- The charge that passes through a given region of area A and length Δx is
- Where n is the number of charge carriers per unit volume and q is the charge carried by each.

27.1

- If the carriers move with a speed of vd, (drift velocity) such that
and

- So the passing charge is also given as

27.1

- If we divide both sides by time we get another expression for average current

27.1

- Drift Velocity-
- Charge carrier: electron
- The net velocity will be in the opposite direction of the E-field created by the battery

27.1

- We can think of the collisions as a sort of internal friction, opposing the motion of the electrons.
- The energy transferred via collision increases the Avg Kinetic Energy, and therefore temperature.
- Quick Quiz p 834
- Example 27.1

27.2 Resistance

- E-Field in a conductor
= 0 when at equilibrium

≠ 0 under a potential difference

- Consider a conductor of cross-sectional area A, carrying a current I.
- We can define a new term called current density
- Units A/m2

27.2

- Because this current density arises from a potential difference across, and therefore an E-field within the conductor we often see
- Many conductors exhibit a Current density directly proportional to the E-field.
- The constant of proportionality σ, is called the “conductivity”

27.2

- This relationship is known as Ohm’s Law.
- Not all materials follow Ohm’s Law
- Ohmic- most conductors/metals
- Nonohmic- material/device does not have a linear relationship between E and J.

27.2

- From this expression we can create the more practical version of Ohm’s Law
- Consider a conductor of length l

27.2

- So the voltage equals
- The term l/σA will be defined as the resistance R, measured in ohms (1 Ω = 1 Volt/Amp)

27.2

- We will define the inverse of the conductivity (σ) as the resistivity (ρ) and is unique for each ohmic material.
- The resistance for a given
ohmic conductor can

be calculated

27.2

- Resistors are very common circuit elements used to control current levels.
- Color Code

27.2

- Quick Quizzes, p. 838-839
- Examples 27.2-27.4

27.4 Resistance and Temperature

- Over a limited temperature range, resistivity, and therefore resistance vary linearly with temperature.
- Where ρis the resistivity at temperature T (in oC), ρo is the resistivity at temperature To, and α is the temperature coefficient of resistivity.
- See table 27.1 pg 837

27.4

- Since Resistance is proportional to resistivity we can also use

27.4

- For most conducting metals the
resistivity varies linearly over a wide

range of temperatures.

- There is a nonlinear region as T
approaches absolute zero where

the resitivity will reach a finite

value.

27.4

- There are a few materials who have negative temperature coefficients
- Semiconductors will
decrease in resistivity

with increasing temps.

- The charge carrier
density increases with

temp.

27.4

- Quick Quiz p 843
- Example 27.6

27.5 Superconductors

- Superconductors- a class of metals and compounds whose resistance drops to zero below a certain temperature, Tc.
- The material often acts like a normal conductor above Tc, but falls of to zero, below Tc.

27.5

- There are basically two recognized types of superconductors
- Metals very low Tc.
- Ceramics much
higher Tc.

27.5

- Electric Current is known to continue in a superconducting loop for YEARS after the applied potential difference is removed, with no sign of decay.
- Applications: Superconducting Magnets (used in MRI)

27.6 Electrical Power

- When a battery is used to establish a current through a circuit, there is a constant transformation of energy.
- Chemical Kinetic Internal (inc. temp)

- In a typical circuit, energy is transferred from a source (battery) and a device or load (resistor, light bulb, etc.)

27.6

- Follow a quanity of charge Q through the circuit below.
- As the charge moves from
a to b, the electric potential

energy increase by U = QΔV,

while the chemical potential

energy decrease by the

same amount.

27.6

- As the charge moves through the resistor, the
system loses this potential

energy due to the collisions

occuring within the

resistor. (Internal/Temp)

- We neglect the resistance
in the wires and assume that

any energy lost between bc

and da is zero.

27.6

- This energy is then lost to the surroundings.
- The rate at which the system energy is delivered is given by
- Power the rate at which the battery delivers energy to the resistor.

27.6

- Applying the practical version of Ohm’s Law (ΔV = IR) we can also describe the rate at which energy is dissipated by the resistor.
- When I is in Amps, V is in Volts, and R is in Ohms, power will be measured in Watts.

27.6

- Quick Quizzes p. 847
- Examples 27.7-27.9

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