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 [1st 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|nAuE The loop rule (Energy conservation) Kirchhoff loop rule [2nd law]: V1 + V2 + V3 + … = 0 along any closed path in a circuit V= U/q  energy per unit charge

Clicker Lamps are identical Batteries are identical In B batteries are connected in series Lamp is brighter in A B 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 2emf  doubles electric field everywhere in the circuit  doubles drift speed  doubles current. Work per second: After getting i for both – ask how much brighter? How much more heat dissipate with 2 batteries? In reality: not 4x because mobility changes with temperature., I.e. current also does not go twice up. eV=eEL loss of electric potential energy (per sec will be power)

Energy in a Circuit Vwire = EL Vbattery = ? From charge conservation and definition of steady state: Node rule – tells us about relations between currents in different parts. But what about actual current? How large is it. To answer – turn to energy conservation principle. Consider one electron as it is transported around the circuit. Energy gained by e as it is transported between terminals in a battery is dissipated in the rest of the circuit. Use round-trip. Energy conservation (the Kirchhoff loop rule [2nd law]): V1 + V2 + V3 + … = 0 along any closed path in a circuit V= U/q  energy per unit charge

Question: Twice the Length 1 2 i1 i2 Nichrome wire (resistive) i1 = i2 i1 = 2*i2 i1 = ½ i2 Electric field is half -> half the drift speed -> half the current. Note that we are considering the wire to be a “resistive” wire.

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 The two bulbs emit “redder” light than the single bulb, indicating that the filaments are not has hot. Here, we consider delta_V to represent the fixed emf of the battery. 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 Parallel In series Identical light bulbs are first connected in series then parallel Will there be a difference in light brightness? There will be no difference In series connection will give brighter light Parallel connection will give brighter light

Two Light Bulbs in Parallel L … length of bulb filament 1. Path ABDFA: 2. Path ACDFA: F iB = iC ibatt = 2iB 3. Path ABDCA: What happens if one light bulb is removed? 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 cross-sectional area of the wire doubles. Electric field in the wire doesn’t change when we use a thicker wire -> current doubles Nichrome wire

Long and Round Bulb in Series only round bulb: Why round bulb does not glow? The calculation in the box shows the electric field required to light the round bulb. The electric field doesn’t produce sufficient current through the filament to make it glow. The round bulb doesn’t light up!

How Do the Currents Know How to Divide? After connection there is a larger current through the battery and a larger gradient of surface charge along the wires to drive this larger current.

Capacitors, Resistors and Batteries Chapter 20 Capacitors, Resistors and Batteries Role of capacitors. Macroscopic analysis complements microscopic analysis Circuits with capacitors – quasi-steady-state – slow rearrangement follows fast initial rearrangement of surface charges.

Electric Field of a Capacitor From lecture 7: E- E+ Enet s z Inside: Fringe: Ask what is R?

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

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. Recall, fringe field is due primarily to charges between the plates.

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. 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. The top figure exaggerates the amount of fringe charge and does not show the charge between the plates. Purple arrows represent the electron current, not Efield! Recall that we derived an expression for the fringe field by considering the superposition of two charged disks separated by a distance s. We ignored the small amount of charge on the exterior of the capacitor.

Capacitor: Charging t=0.1 sec t=1 sec Why does current ultimately stop flowing in the circuit? 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. Equilibrium