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

The Effect of Different Light Bulbs Thick filament Thin filament Which light bulb will glow longer? Why? Ultimately, same amount of charge on capacitor, independent of bulb since no current flowing and voltage diff across capacitor must equal emf. Initially, E through bulb = emf/L. Since L is same for both bulbs, E is same. Current depends on Area, so current in long bulb is less than in round bulb. Experiment: charge 2 capacitors through long and round until they don’t glow. Then discharge both through long and see which gets discharged faster. Round is brighter  capacitor gets charged more? 2) Long bulb glows longer  capacitor gets charged more?

Effect of the Capacitor Disk Size 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? Experiment: charge 2 capacitors through long and round until they don’t glow. Then discharge both through long and see which gets discharged faster. Capacitor 2 has smaller fringe field, so current will be larger (since fringe field opposes current flow). Fringe field:

Effect of the Capacitor Disk Separation In the first moment, which capacitor will cause the bulb to produce more light? Which capacitor will make the light bulb glow longer? Capacitor 2 has smaller fringe field in first moment, so bulb will be brighter. Bulb will glow longer with capacitor 2 since its fringe field is smaller and current ceases to flow when fringe field is large enough to oppose the accumulation of additional charge on the plates. Fringe field:

Effect of Insulator in Capacitor In the first moment, which capacitor will cause the bulb to produce more light? Which capacitor will make the light bulb glow longer? What if we put a metal plate in between? – equivalent to smaller distance. Metal is easily polarized. Fringe field:

The capacitors shown are initially uncharged. When connected to identical circuits, after 0.01 s of charging: The fringe field of each capacitor is the same. The fringe field of the smaller capacitor is greater. The fringe field of the larger capacitor is greater. R1 R2 Larger R, smaller fringe field, so correct answer is B. s s

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 - The current decreases less rapidly in the circuit containing capacitor 1. The current decreases less rapidly in the circuit containing capacitor 2. The current is the same in both circuits. Dielectric decreases E and therefore fringe field is smaller. The fringe field opposes the flow of current. Therefore, the current flows more readily at the same point in time in curcuit 2. B is correct.

Parallel Capacitors Initial moment: brighter? Will it glow longer? Fringe field: Equivalent to doubling the area of the plates of one capacitor. Fringe field will half for the same Q. Therefore bulb will grow longer. Capacitors in parallel effectively increase A

An Isolated Light Bulb Will it glow at all? How do electrons flow through the bulb? Why do we show charges near bulb as - on the left and + on the right? As the capacitors charge, electrons accumulate on the top plate of the right of the right capacitor. These electrons are drawn from the region near the bulb, leaving a deficit of electrons near the right side of the bulb. Recall that due to the lower mobility in the bulb, electrons cannot flow fast enough through the bulb to replace those drawn from the right side. Hence, the charges in the bulb region are as shown. This is also consistent with the direction in which electron current flows.

Capacitor in a Circuit Energy conservation I Charging time Bulb Brightness Energy conservation Do 19.X.7! time Ecap

The Current Node Rule in a Capacitor Circuit Charge conservation: Ii > 0 for incoming Ii < 0 for outgoing …in steady state I1 = I2+ I3 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)

Capacitance -Q +Q Electric field in a capacitor: E In general: s The more charge on the capacitor plates, the bigger the electric field in the gap, and the greater the potential difference across the gap. Capacitance is a measure of the ability to store charge. For a given potential difference, larger C means greater Q. Definition of capacitance: Capacitance of a parallel-plate capacitor: Capacitance

Capacitance Units: C/V, Farads (F) Michael Faraday (1791 - 1867)

Exercise 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 How much charge accumulates on one plate after charging by a circuit with two 1.5 V batteries? Q = 3 C Force between two charges +3C and –3C separated by one meter will be F=9e9*9/1~10^11 N, or 10 million tons How many electrons are there? N=(3 C)/(1.6.10-19 C)  1.9.1019

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

Clicker A B D D C