Last Time Transient response when connecting a circuit

Last Time • • Transient response when connecting a circuit How long until steady state is reached? Kirchhoff's Voltage Loop Law (Difference configuration of circuit). 1

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

Doubling the Cross-Sectional Area If A doubles, the current doubles. Nichrome wire 3

Today • • (Difference configuration of circuit). Charge and discharge capacitors Different way of connecting capacitors. (More details on resistance) 4

i. Clicker Questions When plug in two batteries instead of one, the current will be A. Double B. Halved C. unchanged 5

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: 6

How Do the Currents Know How to Divide? 7

Capacitor: Charging and Discharging Charging Discharging

Capacitor: Construction and Symbols Similar to a large parallel plate 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.

Electric Field of a Capacitor Inside: Enet Fringe: E+ E- s Step 4: check the results: z 0 Units: e r u ct om r F Le 11 6

Capacitor: Discharge Electron Current Electric Field

Capacitor: Charging Fringe field of a capacitor rises until E=0 in a wire – static equilibrium.

Capacitor: Charging 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.

i. Clicker Question. Charging Which of the following is correct? A. The light bulb will glow all the time B. The light will not glow at all C. The light bulb will glow but will grow darker till completely off.

Demos: 6 C-14 Charging and Discharging Capacitors

The Effect of Different Light Bulbs Thin filament Thick 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? After current stops, Voltage across capacitor = Voltage across battery no matter which bulb is used. Capacitor charged by same amount in both cases.

IClicker Question: 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? Fringe field: A. B. C. D. Upper longer, lower brighter Upper longer, upper brighter Lower longer, lower brighter Lower longer, upper brighter

i. Clicker question: 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? Fringe field: A. B. C. D. Upper longer, lower brighter Upper longer, upper brighter Lower longer, lower brighter Lower longer, upper brighter

Effect of Insulator in Capacitor Insulator 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: A. B. C. D. Upper longer, lower brighter Upper longer, upper brighter Lower longer, lower brighter Lower longer, upper brighter

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

An Isolated Light Bulb Will it glow at all? How do electrons flow through the bulb? A. Yes B. No because it’s an open circuit.

The Current Node Rule in a Capacitor Circuit Charge conservation: Ii > 0 for incoming Ii < 0 for outgoing I 1 = I 2+ I 3 …in steady state 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)