Chapter 19 A Microscopic View of Electric Circuits

In steady state current is the same everywhere in a series circuit. ii What is the drift speed? Note: density of electrons n cannot change if same metal What is E? E thick E thin E and Drift Speed

1 mm 0.1 mm v thick = 4  m/s v thin = ? E thin = N/CE thick = ? Exercise v thin = 400  m/s E thick = N/C

Does current fill the wire? Is E uniform across the wire? E must be parallel to the wire E is the same along the wire 00V AB V CD Direction of Electric Field in a Wire

E Bulb filament and wires are metals – there cannot be excess charges in the interior Are excess charges on the battery? E E What charges make the electric field in the wires? Electric Field in a Wire

Van de Graaff generator A Mechanical Battery Electron Current

E E bends Field due to the Battery In the steady state there must be some other charges somewhere that contribute to the net electric field in such a way that the electric field points upstream everywhere. Blue = v drift

Surface charge arranges itself in such a way as to produce a pattern of electric field that follows the direction of the wire and has such a magnitude that current is the same along the wire. Field due to the Battery

Smooth transition from + surface charge to – to provide constant E. E Field due to Battery The amount of surface charge is proportional to the voltage.

The average magnitude of E in a closed circuit can vary from ~.01 V/m in copper wire to more than 100 V/m in Nichrome wire - due to a much different electron mobility. What is easy: to draw E and i What is complex: to draw surface charge distribution Amount of Surface Charge

Connecting a Circuit The initial transient When making the final connection in a circuit, feedback forces a rapid rearrangement of the surface charges leading to the steady state. This period of adjustment before establishing the steady state is called the initial transient.

E net Connecting a Circuit The initial transient Before the gap is closed, the net field in the wire must be zero, because the system is in static equilibrium. E other E gap faces is due to charges on gap faces

Speed of light: 30 cm/ns The initial transient Connecting a Circuit In just a few nanoseconds the rearrangement of the surface charges will extend all the way around the circuit.

1.Static equilibrium: nothing moving (no current) 3.Steady state: constant current (nonzero) 2.Initial transient: short-time process leading to the steady state Connecting a Circuit

Just after connection: E may be the same everywhere After steady state is reached: Surface Charge and Resistors

A Wide Resistor low mobility

Energy conservation (the Kirchhoff loop rule [2 nd law]):  V 1 +  V 2 +  V 3 + … = 0 along any closed path in a circuit  V wire = EL  V battery = ?  V=  U/q  energy per unit charge Energy in a Circuit

non-Coulomb force on each e ECEC FCFC 1. F C =eE C Coulomb force on each e 2. F C =F NC The function of a battery is to produce and maintain a charge separation. Energy input per unit charge emf – electromotive force The emf is measured in Volts, but it is not a potential difference! The emf is the energy input per unit charge. chemical, nuclear, gravitational… Potential Difference Across the Battery Fully charged battery.

The current node rule (Charge conservation) Kirchhoff node or junction rule [1 st law]: In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node Analysis of Circuits  V 1 +  V 2 +  V 3 + … = 0 along any closed path in a circuit The loop rule (Energy conservation) Kirchhoff loop rule [2 nd law]:  V=  U/q  energy per unit charge Conventional current: I = |q|nAuE

Round-trip potential difference: Field and Current in a Simple Circuit We will neglect the battery’s internal resistance for the time being.

Round-trip potential difference: Path 1 Path 2 Field and Current in a Simple Circuit

Nichrome wire (resistive) Question: Twice the Length 12 A)i 1 = i 2 B)i 1 = 2*i 2 C)i 1 = ½ i 2 i1i1 i2i2

Nichrome wire (resistive) Twice the Length Current is halved when increasing the length of the wire by a factor of 2.

Doubling the Cross-Sectional Area Nichrome wire Doubling the cross-sectional area of the wire will A)not change electron current B)increase electron current by 2 C)decrease electron current by 2

Doubling the Cross-Sectional Area Nichrome wire Electron current in the wire increases by a factor of two if the cross- sectional area of the wire doubles. Loop: emf - EL = 0 Can we achieve infinitely large current using very thick wire?

F NC = F C = eE C fully charged Increase mobility – current increases Real battery cannot provide  current Internal battery resistance – limits maximum current Drift speed in battery: fixed Internal Resistance of a Battery We will neglect the battery’s internal resistance for the time being. Approximate  V batt  = emf

The number or length of the connecting wires has little effect on the amount of current in the circuit. u wires >> u filament  Work done by a battery goes mostly into energy dissipation in the bulb (heat).  V Across Connecting Wires