Transcript Angular Momentum and Charge - Artie McFerrin Chemical

Accounting for Charge
Chapter 19
Objectives
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Understand charge and energy
conservation in electrical circuits
Apply Kirchoff's Current and Voltage
Laws
Find equivalent resistances
Understand the concept of charge carrier
Accounting for Charge (q)
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Charge is a property of elementary particles
such as
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Electrons: q = -1, and
Quarks: q = +2/3 or q = -1/3
Combinations of quarks yield:
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Protons: q = +1 = (2/3) + (2/3) + (-1/3)
Neutrons: q = 0 = (2/3) + (-1/3) + (-1/3), and
several others combinations of 2 and 3 quarks
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Protons and neutrons can be considered
elementary particles in our analysis so we can
forget about quarks in the rest of the chapter
Because each type of elementary particles
always carries the same amount of elementary
charge, the total charge for a group of
elementary particles is an extensive quantity.
Certainly, the UAE is applied to each of these
particles independently and so to their charges
UAE for Elementary Charges
q+final - q+initial = q+in - q+out + q+gen - q+cons
q-final - q-initial = q-in - q-out + q-gen - q-cons
To some extent, we can assume that the net charge
in the universe is zero and that generation and
consumption of +ve and –ve charges is concerted,
+ = qq
i.e., gen
gen
q+cons = q-cons
However, the mass of the particle that carries the
+ve charge is different to the mass of the particle
that carries the –ve charge
UAE for elementary charges without
energy-mass transformations
q+final - q+initial = q+in - q+out + q+gen - q+cons
0
0
q-final - q-initial = q-in - q-out + q-gen - q-cons
0
0
UAE for net positive charge (General)
Defining...
qnet,+  q+ - qSubtracting Equation (1) from (2), we get:
q
net , 
final
net , 
initial
q
net , 
in
q
net , 
out
q
UAE for net negative charge (General)
Defining...
qnet,-  q- - q+
Subtracting Equation (1) from (2), we get:
q
net , 
final
net , 
initial
q
net , 
in
q
net , 
in
q
Pairs Problem #1
2 mol of hydrogen (H2) and 1 mol of oxygen
(O2) are placed in a reactor. All of the
hydrogen and oxygen react to form water.
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Initially how many moles of positive charge
are in the reactor? Negative? Net positive?
After the reaction, how many moles of
positive charge are in the reactor? Negative?
Net positive?
Batteries
A battery produces electricity (flow of
electrons) from a chemical reaction.
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Primary battery: once the reactants are
consumed, the battery is dead
Secondary battery: can be recharged
Example: Lead-Acid Battery Discharging
Anode and cathode immersed in sulfuric acid
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Anode (-) made of lead (Pb)
Cathode (+) made of lead oxide (PbO2)
Pb  HSO-4  PbSO4  H   2e (anode)
PbO2  HSO -4  3H   2e   PbSO4  2 H 2O (cathode)
Charging the Battery
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These reactions go the opposite direction
when the battery is being charged.
Some lead sulfate falls to the bottom of the
container instead of collecting on the anode
and cathode.
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Thus, the battery cannot be exactly 100%
charged and will eventually have to be
replaced.
Lead-Acid Battery Charging
Anode and cathode immersed in sulfuric acid
Anode (-) made of lead (Pb)
 Cathode (+) made of lead oxide (PbO2)
Pb  HSO-4  PbSO4  H   2e (anode)
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PbO2  HSO -4  3H   2e   PbSO4  2 H 2O (cathode)
Resistors
Resistors: passive devices that consume electrical
energy. They oppose to the pass of electrons
series
parallel
Current is the same in resistors in series
Voltage is the same in resistors in parallel
Voltage is divide by resistors in series
Current is divided by resistors in parallel
Electrical circuit is a network consisting of a closed loop containing
power sources (current or voltage) and devices such as resistors
Electric Circuits
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i3
i1
An example of a voltage source
is a battery; ideally it should
i2
+
produce a voltage independent
V
of the current
An example of a current source
i2
is a specialized transistor
i3
i1
circuit, which should provide a
i 2 = i1 + i 3
current independent of the
voltage.
By convention: A current is
Remember i = q/t and v = E/q positive when goes in the
Assume the wires have R = 0 opposite direction of the
negative carriers or in the
and V has not internal
direction of the positive
resistance
ones
Kirchoff’s Laws
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Net current at each node is zero (charge
conservation)
Net voltage in each loop is zero (energy
conservation)
Circuit Analysis
iin  iout
i1
i1  i2  i3
V
i2  ,
R2
+
V
i3 
R3
V
 R2  R3 
 1
1

i1  V     V 
 R2 R3 
 R2 R3 
-
i3
i2
R2
R3
Resistors in Parallel
Resistors in parallel can be combined to form the
equivalent resistance
1
1

Req
k Rk
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i
i
+
V
-
i1
i2
i3
R1
R2
R3
+
Req
V
-
Resistors in Series
Resistors in series can also be combined
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Req   Rk
k
+
V
-
i
R2
i
R1
+
R3
Req
V
-
Pairs Exercise #2
Find the equivalent resistance and the total
current in the circuit below.
i
+
5V
-
i1
i2
i3
4 kW
4 kW
2 kW