Make sure your clickers are out and ready before class starts

No homework due this week and no quiz in Fri/Mon recita7ons. Homework #5 is due next Tuesday 16 Oct at 11:59PM We are gegng the exams graded and I will email you when you can look up the results in the gradebook. Make sure your clickers are out and ready before class starts

Chapter 26 Current and Resistance

Up to now we have been considering systems where the arrangement of charges is fixed, studying the electric field produced and its descrip7on by a poten7al func7on. electrosta7cs Rules include Electric field inside a conductor is zero Now we allow charges to move: New quan77es: current, resistance New rules: Ohm s law

The systems we consider have large numbers of charged par7cles moving together Density n = number per volume surface! Velocity v Analogy to fluid flow Near side Far side mass flow rate = mass that passes through surface per 7me = increase in mass on the far side of the surface per 7me Mass flow rate can be posi0ve or nega0ve nega7ve if mass is moving FROM far side TO near side

The systems we consider have large numbers of charged par7cles moving together Density n = number per volume surface Analogy to fluid flow Near side Far side mass flow rate = mass that passes through surface per 7me = increase in mass on the far side of the surface per 7me Electric current = NET charge that passes through surface in a given 7me = increase in charge on the far side of the surface per 7me

Electric current = NET charge that passes through surface per 7me unit 1 C/s = 1 A (Ampere) A number (not a vector) Can be posi7ve or nega7ve Near side surface Far side Posi7ve if net charge on the far side is increasing Nega7ve if net charge on the far side is decreasing

Current = NET charge that passes through surface per 7me = change in net charge on far side of the surface per 7me Far side Far side Far side Far side Scalar: posi7ve or nega7ve Posi7ve charges move to far side: current is posi7ve Posi7ve charges move from far side: current nega7ve nega7ve charges move to far side: current nega7ve nega7ve charges move from far side: current posi7ve

Clicker Of the following four situa7ons in which posi7ve and nega7ve charges move horizontally through a surface at rates shown in the figure, in which situa7on does the current have the smallest magnitude?

Mostly we consider charges moving in metal wires number density n of free charges is a property of the metal (Cu, Al, etc) behaves like incompressible fluid A wire is like a pipe for charge

Consider systems with steady current Current doesn t change with 7me. no buildup or deple7on of charge at any point Analogy with fluids: equa7on of con7nuity i is the same for all cross sec7ons of the wire Split wire: net flow at junc7on is zero i in = i out ; i 0 = i 1 + i 2 Current is NOT a vector

clicker Steady currents flow in the wires shown. What is the magnitude and direc7on of the current i? (a) Zero (b) 2 A, into the junc7on (c) 2 A, out of the junc7on (d) 8 A, into the junc7on (e) 8 A, out of the junc7on

Q: When does current flow through a wire? A: When there is a difference in poten7al between the ends + - Electric field inside the wire -> force that drives the mo7on of charges For + charges, force points from higher electric poten7al to lower Current flows in same direc7on as electric field i

Q: When does current flow through a wire? A: When there is a voltage difference between the ends + - Electric field inside the wire -> force that drives the mo7on of charges But wait: the wire is a conductor Isn t the electric field zero inside a conductor? i

Q: When does current flow through a wire? A: When there is a voltage difference between the ends + - i Electric field inside the wire -> force that drives the mo7on of charges The usual way to create a voltage difference between the ends: Make a circuit with a charged capacitor, a baoery or a power supply q -q

DEMOS Apply a voltage across an object with free charge How do we know a current is flowing? Moving charges collide with atoms in object -> light, heat Current through a wire Free charge = electrons more voltage -> brighter glow (larger current)

DEMOS Apply a voltage across an object with free charge How do we know a current is flowing? Moving charges collide with atoms in object -> light, heat Current through water Dis7lled water Tap water

DEMOS Apply a voltage across an object with free charge How do we know a current is flowing? Moving charges collide with atoms in object -> light, heat Current through a pickle (cucumber in salt water) Free charge = salt ions Na+, Cl-

Q: When does current flow through a wire? A: When there is a voltage difference V between the ends If V increases, expect I to increase. If I is propor7onal to V, then the object obeys Ohm s law Ra7o V/I is called the resistance R of the object Resistance characteris7c of the object (length of wire, cross sec7onal area, material it s made out of, temperature) Unit 1 V/A = 1 Ohm

DEMOS Apply a voltage across an object with free charge Measure current with an ammeter Find resistance of object V = I R so R = slope of the plot of V vs I.

The resistance of an object depends on the temperature

DEMOS Object = coil of copper wire Apply a voltage across the coil Measure current by brightness of the light bulb Cool down the copper wire with liquid nitrogen What happens to the resistance of the coil? What happens to the current through the coil?

Energy and power Charges move downhill in poten7al: poten7al energy decreases + - Current at the two ends is equal velocity of moving charges is the same at two ends kine7c energy doesn t charge Therefore, the total energy of the moving charges decreases (like the box moving with kine7c fric7on in prelecture) energy is lost to heat and light i

Energy and power Charges move downhill in poten7al: poten7al energy decreases + - du = dq V = I V dt (du is the magnitude of the decrease) du/dt = P = iv If system obeys Ohm s law, can also write P=i 2 R = V 2 /R DEMO: burning resistor i