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Quiz 7 was thRs.Nov.21 Tue.Dec.03
... see Quiz 7 key as *.jpg

Topic 7 (Electricity)

where we re-do the first 4 topics, but watch electric charge, rather than mass

Electric charge comes in TWO kinds : Positive (protons) and Negative (electrons) ... the total is conserved !
=> q_object   =   N e   . . .   integer Number of "elementary charges" e

charge in motion   q v   is called Indicated Electric Current . . . (+)→ and ←(−) both are   I →
=> I = ΔQ / Δt   ~ ρ v A   ... 1 C/s is called an Ampere ... it is similar to momentum as mass flow

Electric charge is pushed or pulled by the Electric Field   E . . . like mass is pulled by a gravity field

Positive charges carry Electric Field that points outward, away from themselves
      in the direction that a (+) proton would be pushed .
. . . the Electric field intensity weakens with distance ... as 1/distance squared
      since the Electric field (out farther) spreads over a bigger surface Area (like a planet's Gravity field).
. . . negative charges carry Electric Field that points inward, toward themselves
      in the direction that a (+) proton would be pulled .
=> E = k Q /d ²   . . . k = Coulomb's constant = 9E9 Nm²/C² .

Electric Field extends through space from positive electric charge to negative electric charge

When we separate positive charges from negative charges, we stretch this Electric Field
. . . this puts Tension in the space between the charges
      this requires us to do Work ... which puts Energy in the new charge configuration
. . . we might think of it as moving one of the charges along the Electric field (that is caused by the other charge)
      the Electric Field points "downhill", toward lower PE for positive charge (analogous to gh in mechanical world)
      so if we move the positive charge away from the negative one, we move it "uphill"
=> W = F·d = (q E)·d = q (E·d) = q ΔV   . . . charge moved thru a difference in Potential

Electric field Units : 1 Newton/Coulomb = 1 Volt/meter

Electric Potential   V   is the environment part ("aspect") of Electric Potential Energy   q V

Positive charges are surrounded by positive Electric Potential   V
      so a proton nearby would have positive electric Potential Energy
. . . but an electron nearby would have negative electric PE
      electrons are usually trapped (with negative PE) in the electric PE well of their atom
      ... like planets are trapped in the Gravity PE well of their Sun.

Negative charges are surrounded by negative Electric Potential   V
      so a proton nearby would have negative electric Potential Energy
. . . but an electron nearby would have positive electric PE
      and could be pushed away, trading this (+) PE for (+) KE farther away.
=> PE_electric = q V   . . . 1 Joule = 1 Coulomb·Volt

here's a 2-dimensional graph of the Electric Potential (vertical axis)       near a positive charge (left) and a negative charge (right) everywhere on the left half has positive Potential . . . because it is closer to the positive charge       V = k Q / r the right side is closer to the negative charge . . . so the V there is negative V = 0 all along center-line , midway between the charges . . . there, the +V contributed by the positive charge       is cancelled by the −V that the negative charge contributes. => V contributions   add . . . it is a quantity describing the location (the environment there)

Power : the rate that charge carries Energy

A fresh battery has a lot of (+) PE because it has excess protons (+q) near the (+)V end,
      and also a lot of excess electrons (−q) near the (−)V end.
. . . in use, electrons leave the (−)V end with   (−e)(−V) = (+)PE,
      and eventually enter the (+) end with   (−e)(+V) = (−)PE .
It is the difference in potential (one end − the other) that is the voltage, which describes the "electrical landscape".
      the Electric Field is the gradient   (slope, distance-wise)   of the potential , so that's what determines how fast the charge flows.
. . . connect a really long wire to both sides of a battery, and the potential gradient along it will be very shallow, so very slow current
      connect that drop via a short route, and the current might be so fast as to melt its insulation off!

if there are 2 routes from high PE to low PE, some charge will take each route ... more will take the steeper or wider wire
. . . the current that enters the split is the same total current after the split − it is just split
      the shorter filament wire with big Area conducts well , so it presents low resistance to charge flow
=> most of the current takes the path of least resistance

. . . if there are 2 obstacles (light bulbs) in one path (from high to low), the 2 voltages ("electric height" drops) must add to be the total voltage
      current will flow ½ as fast (I = ½ I₁) because each bulb (filament length) can only be half as steep ... since their voltages add.
=> I = V /R   . . . where R is the Resistance to flow ... "obstacle-ness" ... Resistances in series add ... since the same current flows thru both bulbs!

sort-of-optional: more about electrical resistance

You may think of resistance as electric friction, transforming electric PE into Thermal TE
      the faster the current goes thru, the faster the Energy gets "lost to friction" ... since Power = ΔE/Δt ,
=> Power = I·V   . . . Watt = Amp·Volt .

resistance depends on the length of the conductor × how hard that kind of material is to go thru
. . . conductance ... 1/resistance ... depends on the Area that the electrons can go thru
=> R = resistivity * L / A . . . resistivity is a material property (look up in a table) but it changes with Temperature

Resistances in series add ... because their lengths add
      2 resistors in series exert 2× the resistance (to current flow) as one did
. . . resistances in parallel are reduced ... conductances in parallel add ... because their Areas add
      3 resistors in parallel exert 1/3 as much resistance as one did