Chapter 19 A Microscopic View of Electric Circuits

Chapter 19 A Microscopic View of Electric Circuits

Analysis of Circuits 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 Conventional current: I = |q|n. Au. E The loop rule (Energy conservation) Kirchhoff loop rule [2 nd law]: V 1 + V 2 + V 3 + … = 0 along any closed path in a circuit V= U/q energy per unit charge

Clicker A B Lamps are identical Batteries are identical In B batteries are connected in series Lamp is brighter in A) A B) B C) Lamps in A and B have the same brightness

Two Batteries in Series Why light bulb is brighter with two batteries? Two batteries in series can drive more current: Potential difference across two batteries in series is 2 emf doubles electric field everywhere in the circuit doubles drift speed doubles current. Work per second: e V=e. EL loss of electric potential energy (per sec will be power)

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

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

Two Identical Light Bulbs in Series Two identical light bulbs in series are the same as one light bulb with twice as long a filament. Identical light bulbs Electron mobility in metals decreases as temperature increases! Conversely, electron mobility in metals increases as temperature decreases. Thus, the current in the 2 -bulb circuit is slightly more than that in the ½ of one-bulb circuit.

Question: Two Light Bulbs In series Parallel Identical light bulbs are first connected in series then parallel Will there be a difference in light brightness? A) There will be no difference B) In series connection will give brighter light C) Parallel connection will give brighter light

Two Light Bulbs in Parallel L … length of bulb filament 1. Path ABDFA: 2. Path ACDFA: 3. Path ABDCA: F i. B = i C ibatt = 2 i. B We can think of the two bulbs in parallel as equivalent to increasing the cross-sectional area of one of the bulb filaments.

Doubling the Cross-Sectional Area Loop: emf - EL = 0 Electron current in the wire increases by a factor of two if the crosssectional area of the wire doubles. Nichrome wire

Long and Round Bulb in Series only round bulb: The round bulb doesn’t light up!

How Do the Currents Know How to Divide?

Chapter 20 Capacitors, Resistors and Batteries

Electric Field of a Capacitor From lecture 7: Inside: Enet E+ E- Fringe: s 0 z

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

How is Discharging Possible? Positive and negative charges are attracted to each other: how can they leave the plates? Fringe field is not zero! 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.

Capacitor: Discharge The fringe field of the capacitor plus the electric field of the charges on the surface of the wires drive current in a way to REDUCE the charge of the capacitor plates.

Capacitor: Charging t=0. 1 sec t=1 sec Why does current ultimately stop flowing in the circuit? Equilibrium Ultimately, the fringe field of the capacitor and the field due to charges on the wire are such that E=0 inside the wire. At this point, i=0.