Chapter 17

Chapter 17. Current and Resistance. A Bit of History. Ancient Greeks Observed electric and magnetic phenomena as early as 700 BC Found that amber, when rubbed, became electrified and attracted pieces of straw or feathers Magnetic forces were discovered by observing magnetite attracting iron.

Chapter 17Current and ResistanceA Bit of History

Ancient Greeks

Observed electric and magnetic phenomena as early as 700 BC

Found that amber, when rubbed, became electrified and attracted pieces of straw or feathers

Magnetic forces were discovered by observing magnetite attracting iron

Properties of Electric Charges

Two types of charges exist

They are called positive and negative

Named by Benjamin Franklin

Like charges repel and unlike charges attract one another

Nature’s basic carrier of positive charge is the proton

Protons do not move from one material to another because they are held firmly in the nucleus

More Properties of Charge

Nature’s basic carrier of negative charge is the electron

Gaining or losing electrons is how an object becomes charged

Electric charge is always conserved

Charge is not created, only exchanged

Objects become charged because negative charge is transferred from one object to another

Properties of Charge, final

Charge is quantized

All charge is a multiple of a fundamental unit of charge, symbolized by e

Quarks are the exception

Electrons have a charge of –e

Protons have a charge of +e

The SI unit of charge is the Coulomb (C)

e = 1.6 x 10-19 C

Ex. 1

A typical lightning bolt has about 10.0C of charge. How many excess electrons are in a typical lightning bolt?

Fig. 15.T1, p. 472Conductors

Conductors are materials in which the electric charges move freely

Copper, aluminum and silver are good conductors

In terms of circuits, we will generally be using copper

When a conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material

Electric Current

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

Current (I) = units of charge (Q) per time

I = Q/t

The SI unit of current is Ampere (A)

1 A = 1 C/s

Ex. 1

The amount of charge that passes through the filament of a certain light bulb in 2.00s is 1.67C.

A) Determine the current in the light bulb.

B) How many electrons passed through the filament per second?

Ex. 2

A 100.0 W light bulb draws 0.83A of current. How many electrons pass a given cross-sectional area of the filament in 1 hour?

Ex. 3

1.5 x 107 electrons pass through a given cross section of a wire every 1.0s.

A) Find the current in the wire.

B) How much charge (in C) passes through the wire per minute?

Analogy to Flow of Water

Electric Charge = Water

Coulomb = Gallons of Water

Electron = Molecule of Water

Electric Current = Rate of Water Flow

Ampere = Gallons of Water per second

Potential Difference or Voltage = Water Pressure (height of waterfall)

Wire = Riverbed

Resistance = Rocks in the River

Electric Current, cont

When diagramming, conventional current flowis the direction positive charge (+) would flow

This is known as conventional current flow

In a common conductor, such as copper, the actual current is due to the motion of the negatively charged electrons

In a particle accelerator, positively charged protons are set in motion

Electrical Energy and Power, final

The SI unit of power is Watt (W)

The unit of energy used by electric companies is the kilowatt-hour (kW-hr)

This is defined in terms of the unit of power and the amount of time it is supplied

1 kWh = 3.60 x 106 J

Meters in a Circuit -- Ammeter

An ammeter is used to measure current

In line with the bulb, all the charge passing through the bulb also must pass through the meter

Meters in a Circuit -- Voltmeter

A voltmeter is used to measure voltage (potential difference)

Connects to the two ends of the bulb

Which will turn the bulb on?

A.

B.

C.

D.

Drift Velocity

Drift Velocity is the velocity at which electrons move opposite the electric field (E).

Counterintuitively, drift velocity is very small. (eg 2.46 x 10-4 m/s in Cu wire)

So how does the electric light turn on so quickly??? Hmmmmm…

Charge Carrier Motion in a Conductor

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

Resistance

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

Resistance, cont

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 (analogous to water colliding with rocks in a river)

Ohm’s Law

In general, resistance remains constant over a wide range of applied voltages or currents

This statement has become known as Ohm’s Law

ΔV = I R

Factors affecting resistance

Length of a resistor – R increases with length (directly prop.)

Cross-sectional area – R increases with smaller cross-sectional area (inv. prop.)

Material – different metals have different resistances

Temperature – R increases with temperature (dir. prop.)

Superconductors

A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, TC

TC is called the critical temperature

Superconductors, cont

Once a current is set up in a superconductor, it persists without any applied voltage

Since R = 0

Superconductor Timeline

1911

Superconductivity discovered by H. Kamerlingh Onnes

1986

High temperature superconductivity discovered by Bednorz and Müller

Superconductivity near 30 K

1987

Superconductivity at 96 K and 105 K

Current

More materials and more applications

Electrical Energy and Power, cont

The rate at which the energy is lost in a circuit is the power

From Ohm’s Law, alternate forms of power are

For the two resistors shown here, rank the currents at points a through f, from largest to smallest.QUICK QUIZ 17.6Ia = Ib > Ic = Id > Ie = If . Charges constituting the current Ialeave the positive terminal of the battery and then split to flow through the two bulbs; thus, Ia= Ic+ Ie. Because the potential difference ΔV is the same across the two bulbs and because the power delivered to a device is P = I(ΔV), the 60–W bulb with the higher power rating must carry the greater current. Because charge does not accumulate in the bulbs, all the charge flowing into a bulb from the left has to flow out on the right; consequently Ic= Idand Ie= If. The two currents leaving the bulbs recombine to form the current back into the battery, If + Id= Ib.QUICK QUIZ 17.6 ANSWERTwo resistors, A and B, are connected across the same potential difference. The resistance of A is twice that of B. (a) Which resistor dissipates more power? (b) Which carries the greater current?QUICK QUIZ 17.7B, B. Because the voltage across each resistor is the same, and the rate of energy delivered to a resistor is P = (ΔV)2/R, the resistor with the lower resistance exhibits the higher rate of energy transfer. In this case, the resistance of B is smaller than that for A and thus B dissipates more power. Furthermore, because P = I(ΔV), the current carried by B is larger than that of A.QUICK QUIZ 17.7 ANSWERElectrical Activity in the Heart

Every action involving the body’s muscles is initiated by electrical activity

Voltage pulses cause the heart to beat

These voltage pulses are large enough to be detected by equipment attached to the skin

Electrocardiogram (EKG)

A normal EKG

P occurs just before the atria begin to contract

The QRS pulse occurs in the ventricles just before they contract

The T pulse occurs when the cells in the ventricles begin to recover

Abnormal EKG, 1

The QRS portion is wider than normal

This indicates the possibility of an enlarged heart

Abnormal EKG, 2

There is no constant relationship between P and QRS pulse

This suggests a blockage in the electrical conduction path between the SA and the AV nodes

This leads to inefficient heart pumping

Abnormal EKG, 3

No P pulse and an irregular spacing between the QRS pulses

Symptomatic of irregular atrial contraction, called fibrillation

The atrial and ventricular contraction are irregular

Implanted Cardioverter Defibrillator (ICD)

Devices that can monitor, record and logically process heart signals

Then supply different corrective signals to hearts that are not beating correctly