chapter 27 current and resistance. intro up until now, our study of electricity has been focused...
TRANSCRIPT
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 passingperpendicularly through a given area.
27.1
• The average current
• The instantaneous current
• The SI unit of current is the Ampere (A)
t
QIavg
dt
dQI
s 1
C 1A 1
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.
qxnAQ
27.1
• If the carriers move with a speed of vd, (drift velocity) such that
and
• So the passing charge is also given as
t
xvd
tvx d
qtnAvQ d
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 dnqA
IvJ
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”
EJ
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
EV
V
EJ
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)
IRA
IJ
V
I
VR
IRV
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
AR
27.4 Resistance and Temperature
• Over a limited temperature range, resistivity, and therefore resistance vary linearly with temperature.
• Where ρ is 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
oo TT 1
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.
27.5 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, thesystem 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.
VIVdt
dQVQ
dt
d
dt
dU
VIP
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.
R
VRIP
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