Chapter 26
• Battery
o Carbon electrode (+) on + terminus and Zinc electrode (-) on – terminus
§ In sulfuric acid
§ Acid attacks the Zinc on the surface of the rod and oxidizes it
§ Amount of zinc determines life of battery
o emf or ℇ determined by type of chemical reaction
o Capacity determined by total amount of chemicals
§ In Amp-hours
§ Total charge a battery can move from – terminal to + terminal at given
emf
• Amount of zinc that can go from one side to the other side
• ∆𝑄 = 𝐼∆𝑡 = 𝐴 ∗ ℎ (Amp-hours)
§ At Zn electrode: 𝑍𝑛 → 𝑍𝑛!" + 2𝑒 #
• 𝑉$ − 𝑉% = 0.76𝑉
§ At C electrode: 𝑍𝑛!" + 2𝑒 # → 𝑍𝑛
• 𝑉$ − 𝑉& = −0.76𝑉
§ 𝑒𝑚𝑓 = 0.76 − (−0.76) = 1.52𝑉
§ 𝑒𝑚𝑓 = 1.52𝑉
o Internal resistance (r) determined by size and materials
§ At Zn electrode: 𝑍𝑛 → 𝑍𝑛!" + 2𝑒 #
• 𝑉$ − 𝑉% = 0.76𝑉
§ At C electrode: 𝑍𝑛!" + 2𝑒 # → 𝑍𝑛
• 𝑉′$ − 𝑉& = −0.76𝑉
§ Ohm’s Law: 𝑉$ − 𝑉 ' & = 𝐼𝑅
§ Terminal Voltage: 𝑉& − 𝑉% = 1.52𝑉 − 𝐼𝑅
• 𝑉()*+,-./ = 𝑒𝑚𝑓 − 𝐼𝑅
§ 𝑉 = 𝑒𝑚𝑓 for voltage of a battery
§ If you see __V battery, it means emf
o Ex: The capacity of 1.5V battery is rated at 100 Amp-hours. How much electric
energy can it deliver?
§ 100 Amp-hours is 100 Amps in 1 hour
§ ∆𝑄 = 𝐼∆𝑡
§ ∆𝑄 = (100)(1 ∗ 60 ∗ 60)
• Multiply 1 hour by 3600sec to get seconds
§ ∆𝑄 = 3.6 ∗ 100
§ ∆𝑈 = ∆𝑄 ∗ 𝑉
§ 𝑉 = 𝑒𝑚𝑓
§ ∆𝑈 = (3.6 ∗ 100 )(1.5)
§ 5.4 * 105 J
o Need higher energy density materials for lighter battery
§ More energy in less amount of metal
§ Lithium > Zinc for energy density
, o Ex: What is the internal resistance of a 12V battery whose terminal voltage drops
8.4V when the starter draws 95A? What is the resistance of the starter?
§ 𝑉()*+,-./ = 𝑒𝑚𝑓 − 𝐼𝑅
1 #)+2
§ 𝑅 = − !"#$%&'( 3
4.6#7!
§ 𝑅=− 80
§ 0.038 W
• Circuit
o
§ Straight lines are not resistors
§ Squiggly things mean resistors
§ Battery is the two uneven sized lines
• If battery has resistance, we need a squiggly
o Resistance in a circuit is lumped into resistors
o Connecting wires have no resistance
§ Shape/length not important
o Functions of connecting wires
§ Provide pathways for current flow
§ Set the potentials along the wires at the same level
o
§ Same circuitry: 2 resistors in parallel
§ Parallel means attractive force
o
§ Same circuitry: 2 and 2 resistors in parallel
• Series and Parallel Combinations of Resistors
9ℓ
o 𝑅= ;
§ Resistance proportional to length
§ Longer = more resistance
o Resistors in series
, §
§ Longer pathway by adding resistors
§ Current: 𝐼7 = 𝐼! = 𝐼<
• Current same through each resistor
§ Voltage: 𝑉 = 𝑉7 + 𝑉! + 𝑉<
§ Equivalent resistance: 𝑅)= = 𝑅7 + 𝑅! + 𝑅<
o Resistors in parallel
§
§ Wider pathway by adding resistors
§ Current: 𝐼 = 𝐼7 + 𝐼! + 𝐼<
§ Voltage: 𝑉7 = 𝑉! = 𝑉<
• Voltage same across each resistor
7 7 7 7
§ Equivalent resistance: > = > + > + >
") * + ,
7
• 𝑅)= = * * *
" "
-* -+ -,
o Ex: Suppose that you have a 680Ω, a 720Ω, and a 1.2kΩ resistor. What is the
maximum and minimum resistance you can obtain by combining these?
§ Maximum
• Maximum is in series
• 𝑅)= = 𝑅7 + 𝑅! + 𝑅<
• 𝑅)= = 680 + 720 + 1200
• 2600𝛀
§ Minimum
• Minimum is in parallel
7
• 𝑅)= = * * *
" "
-* -+ -,
7
• 𝑅)= = * * *
" "
./0 1+0 *+00
7
• 𝑅)= = ?.??<@
• 270.8𝛀
o Ex: Consider the network of resistors shown below. What happens to the voltage
across each resistor when the switch (S) is closed? What happens to the current
through each when the switch is closed? What happens to the power output of
the battery when the switch is closed? Let 𝑅7 = 𝑅! = 𝑅< = 𝑅6 = 125Ω and 𝑉 =
22V. Determine the current through each resistor before and after closing the
switch.
• Battery
o Carbon electrode (+) on + terminus and Zinc electrode (-) on – terminus
§ In sulfuric acid
§ Acid attacks the Zinc on the surface of the rod and oxidizes it
§ Amount of zinc determines life of battery
o emf or ℇ determined by type of chemical reaction
o Capacity determined by total amount of chemicals
§ In Amp-hours
§ Total charge a battery can move from – terminal to + terminal at given
emf
• Amount of zinc that can go from one side to the other side
• ∆𝑄 = 𝐼∆𝑡 = 𝐴 ∗ ℎ (Amp-hours)
§ At Zn electrode: 𝑍𝑛 → 𝑍𝑛!" + 2𝑒 #
• 𝑉$ − 𝑉% = 0.76𝑉
§ At C electrode: 𝑍𝑛!" + 2𝑒 # → 𝑍𝑛
• 𝑉$ − 𝑉& = −0.76𝑉
§ 𝑒𝑚𝑓 = 0.76 − (−0.76) = 1.52𝑉
§ 𝑒𝑚𝑓 = 1.52𝑉
o Internal resistance (r) determined by size and materials
§ At Zn electrode: 𝑍𝑛 → 𝑍𝑛!" + 2𝑒 #
• 𝑉$ − 𝑉% = 0.76𝑉
§ At C electrode: 𝑍𝑛!" + 2𝑒 # → 𝑍𝑛
• 𝑉′$ − 𝑉& = −0.76𝑉
§ Ohm’s Law: 𝑉$ − 𝑉 ' & = 𝐼𝑅
§ Terminal Voltage: 𝑉& − 𝑉% = 1.52𝑉 − 𝐼𝑅
• 𝑉()*+,-./ = 𝑒𝑚𝑓 − 𝐼𝑅
§ 𝑉 = 𝑒𝑚𝑓 for voltage of a battery
§ If you see __V battery, it means emf
o Ex: The capacity of 1.5V battery is rated at 100 Amp-hours. How much electric
energy can it deliver?
§ 100 Amp-hours is 100 Amps in 1 hour
§ ∆𝑄 = 𝐼∆𝑡
§ ∆𝑄 = (100)(1 ∗ 60 ∗ 60)
• Multiply 1 hour by 3600sec to get seconds
§ ∆𝑄 = 3.6 ∗ 100
§ ∆𝑈 = ∆𝑄 ∗ 𝑉
§ 𝑉 = 𝑒𝑚𝑓
§ ∆𝑈 = (3.6 ∗ 100 )(1.5)
§ 5.4 * 105 J
o Need higher energy density materials for lighter battery
§ More energy in less amount of metal
§ Lithium > Zinc for energy density
, o Ex: What is the internal resistance of a 12V battery whose terminal voltage drops
8.4V when the starter draws 95A? What is the resistance of the starter?
§ 𝑉()*+,-./ = 𝑒𝑚𝑓 − 𝐼𝑅
1 #)+2
§ 𝑅 = − !"#$%&'( 3
4.6#7!
§ 𝑅=− 80
§ 0.038 W
• Circuit
o
§ Straight lines are not resistors
§ Squiggly things mean resistors
§ Battery is the two uneven sized lines
• If battery has resistance, we need a squiggly
o Resistance in a circuit is lumped into resistors
o Connecting wires have no resistance
§ Shape/length not important
o Functions of connecting wires
§ Provide pathways for current flow
§ Set the potentials along the wires at the same level
o
§ Same circuitry: 2 resistors in parallel
§ Parallel means attractive force
o
§ Same circuitry: 2 and 2 resistors in parallel
• Series and Parallel Combinations of Resistors
9ℓ
o 𝑅= ;
§ Resistance proportional to length
§ Longer = more resistance
o Resistors in series
, §
§ Longer pathway by adding resistors
§ Current: 𝐼7 = 𝐼! = 𝐼<
• Current same through each resistor
§ Voltage: 𝑉 = 𝑉7 + 𝑉! + 𝑉<
§ Equivalent resistance: 𝑅)= = 𝑅7 + 𝑅! + 𝑅<
o Resistors in parallel
§
§ Wider pathway by adding resistors
§ Current: 𝐼 = 𝐼7 + 𝐼! + 𝐼<
§ Voltage: 𝑉7 = 𝑉! = 𝑉<
• Voltage same across each resistor
7 7 7 7
§ Equivalent resistance: > = > + > + >
") * + ,
7
• 𝑅)= = * * *
" "
-* -+ -,
o Ex: Suppose that you have a 680Ω, a 720Ω, and a 1.2kΩ resistor. What is the
maximum and minimum resistance you can obtain by combining these?
§ Maximum
• Maximum is in series
• 𝑅)= = 𝑅7 + 𝑅! + 𝑅<
• 𝑅)= = 680 + 720 + 1200
• 2600𝛀
§ Minimum
• Minimum is in parallel
7
• 𝑅)= = * * *
" "
-* -+ -,
7
• 𝑅)= = * * *
" "
./0 1+0 *+00
7
• 𝑅)= = ?.??<@
• 270.8𝛀
o Ex: Consider the network of resistors shown below. What happens to the voltage
across each resistor when the switch (S) is closed? What happens to the current
through each when the switch is closed? What happens to the power output of
the battery when the switch is closed? Let 𝑅7 = 𝑅! = 𝑅< = 𝑅6 = 125Ω and 𝑉 =
22V. Determine the current through each resistor before and after closing the
switch.
