Chapter 20 A Microscopic View of Electric Circuits

The capacitor in your set is similar to a large two-disk capacitor s D Capacitor: Construction and Symbols There is no connecting path through a capacitor

Positive and negative charges are attracted to each other: how can they leave the plates? Fringe field is not zero! How is Discharging Possible? Electrons in the wire near the negative plate feel a force that moves them away from the negative plate. Electrons near the positive plate are attracted towards it.

A B C D

Thick filamentThin filament Which light bulb will glow longer? Why? 1)Round is brighter  capacitor gets charged more? 2)Long bulb glows longer  capacitor gets charged more? The Effect of Different Light Bulbs

Use two different capacitors in the same circuit In the first moment, which capacitor will cause the bulb to produce more light? Which capacitor will make the light bulb glow longer? Fringe field: Effect of the Capacitor Disk Size

In the first moment, which capacitor will cause the bulb to produce more light? Fringe field: Which capacitor will make the light bulb glow longer? Effect of the Capacitor Disk Separation

In the first moment, which capacitor will cause the bulb to produce more light? Fringe field: Which capacitor will make the light bulb glow longer? Insulator Effect of Insulator in Capacitor

Consider two capacitors whose only difference is that capacitor number 1 has nothing between the plates, while capacitor number 2 has a layer of plastic in the gap. They are placed in two different circuits having similar batteries and bulbs in series with the Capacitor. In the first fraction of a second - A)The current decreases less rapidly in the circuit containing capacitor 1. B)The current decreases less rapidly in the circuit containing capacitor 2. C)The current is the same in both circuits.

Initial moment: brighter? Will it glow longer? Parallel Capacitors Fringe field: Capacitors in parallel effectively increase A

Will it glow at all? How do electrons flow through the bulb? An Isolated Light Bulb Why do we show charges near bulb as - on the left and + on the right?

Connecting Capacitor Parallel to a Battery

I 1 = I 2 + I 3 Charge conservation: I i > 0 for incoming I i < 0 for outgoing Capacitor transients: not a steady state! Cannot use Kirchhoff rule for a part of a capacitor (area 1 or 2) But can use for capacitor as a whole (area 3) The Current Node Rule in a Capacitor Circuit …in steady state

Electric field in a capacitor: E s +Q -Q In general: Definition of capacitance: Capacitance Capacitance of a parallel- plate capacitor: Capacitance

Michael Faraday ( ) Units: C/V, Farads (F)

The capacitor in your set is equivalent to a large two-disk capacitor s=1 mm D How large would it be? D ~ 10 km (6 miles) Exercise

A capacitor is formed by two rectangular plates 50 cm by 30 cm, and the gap between the plates is 0.25 mm. What is its capacitance? Exercise

s D No insulator:With insulator: A Capacitor With an Insulator Between the Plates

How much charge accumulates on one plate after charging by a circuit with two 1.5 V batteries? Q = 3 C How many electrons are there? N=(3 C)/( C)  Exercise

Microscopic treatment: insight into the fundamental physical mechanism of circuit behavior. Not easy to measure directly E, u, Q, v. It is easier to measure conventional current, potential difference  macroscopic parameters Need a link between microscopic and macroscopic quantities. Macroscopic Analysis of Circuits

Many elements in a circuit act as resistors: prevent current from rising above a certain value. Goal: find a simple parameter which can predict  V and I in such elements. Need to combine the properties of material and geometry. Resistance

Conventional current: Different properties of the material Geometry Group the material properties together: Current density: Conductivity Combining the properties of a material

In copper at room temperature, the mobility of electrons is about (m/s)/(V/m) and the density of electrons is n= m -3. What is  ? What is the strength of E required to drive a current of 0.3 A through a copper wire which has a cross-section of 1 mm 2 ? Exercise

The conductivity of tungsten at RT is  = (A/m 2 )/(V/m) and it decreases 18 times at a temperature of a glowing filament (3000 K). The tungsten filament has a radius of mm. What is E required to drive 0.3A through it? Exercise

Conductivity with two Kinds of Charge Carriers

Conventional current: Widely known as Ohm’s law Resistance of a long wire: Units: Ohm,  George Ohm ( ) Resistance Resistance combines conductivity and geometry!

Microscopic Macroscopic Can we write V=IR ? Microscopic and Macroscopic View Current flows in response to a  V

L=5 mm A = mm 2 Conductivity of Carbon:  = (A/m 2 )/(V/m) What is its resistance R? (V/A) What would be the current through this resistor if connected to a 1.5 V battery? Exercise: Carbon Resistor

Mobility of electrons: depends on temperature Conductivity and resistance depend on temperature. Conductivity may also depend on the magnitude of current. Constant and Varying Conductivity