Chapter 1-5 Review: Batteries, Cells, Amp Hours, and Basic Circuits
Circuit context: max current in the solar circuit
The discussion starts with the supply minus the voltage drop across the diode, yielding a total of 6.9 V across R1.
Given R1 = 130 Ω, the current is calculated as
I = rac{V}{R} \,=\, \frac{6.9\text{ V}}{130\ \Omega} \approx 0.053\text{ A} = 53\ \text{mA}.This 53 mA represents the maximum current the solar circuit can deliver through the series path.
When the current through R2 reaches about 53 mA, the voltage will start to drop because the circuit can no longer sustain additional current without voltage degradation at the junction.
In a simple series circuit, current from the source follows Kirchhoff's current law: the current out of the power supply equals the current through R1, i.e. the series current is the same everywhere in the loop.
The lecturer uses a thought experiment to illustrate making a battery from everyday items (penny, nail, etc.) and the need for an electrolyte and a solution to complete the circuit; emphasizes practical setup and measurement with a multimeter.
Battery terminology: cells vs. batteries; voltage basics
A “cell” is a single electrochemical cell consisting of electrolyte and two dissimilar metals; a “battery” is a collection of one or more cells.
A 9-volt battery is typically a stack of multiple smaller cells inside, not a single 9 V cell.
A typical 1.5 V cell (e.g., AA) is one cell; a nickel-metal hydride (NiMH) rechargeable cell is also about 1.2 V.
In contrast, a 9 V battery uses multiple cells in series to achieve the higher voltage; the number of stacked cells, not the physical size alone, determines the voltage.
The speaker notes a Li-ion cell can have nominal voltages around 3.7 V (with variations by chemistry and temperature). The exact voltage depends on the material and electrolyte and temperature.
The point is reinforced: size does not determine voltage; chemistry and the number of cells determine voltage.
The statue/galvanic corrosion anecdote is tied to real-world corrosion issues (copper skin on the Statue of Liberty) illustrating why electrolytes and insulating layers (shellac, PTFE) are important in preventing electrochemical wear.
Reduction, oxidation, and redox concepts in a copper–zinc cell
Redox (reduction-oxidation) reactions do not happen in isolation; they occur as a couple in electrochemical cells.
In a copper–zinc cell, two half-cells are connected by a salt bridge; electrons flow from the zinc anode to the copper cathode.
Oxidation at the anode (zinc):
\text{Zn} \rightarrow \text{Zn}^{2+} + 2e^-.Reduction at the cathode (copper):
\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}.Current I and electron flow are often represented by e⁻; the flow of electrons goes from the anode to the cathode through the external circuit.
The electrode potentials (in the lecture’s example): $E^\circ{\text{Zn}^{2+}/\text{Zn}} \approx -0.76\ \text{V}$ and $E^\circ{\text{Cu}^{2+}/\text{Cu}} \approx +0.34\ \text{V}$.
The cell potential is:
E{\text{cell}} = E^\circ{\text{cathode}} - E^\circ_{\text{anode}} = 0.34 - (-0.76) \approx 1.10\ \text{V}.The 1.10 V value arises because copper releases electrons at a slower rate (less negative tendency) than zinc, so zinc supplies electrons more readily.
Temperature and solution composition affect redox potentials and thus the measured cell voltage.
For lithium-based cells, the nominal voltage is cited around 3.35 V (with variations by temperature and electrolyte); other chemistries (e.g., Li–O2) can yield higher potentials depending on materials.
The redox concept helps explain why different metals in different electrolytes yield different voltages and why some metals corrode preferentially in certain environments.
Battery concepts: from cells to packs; voltage, capacity, and energy
A battery’s voltage is determined by the chemistry of its cells and how many cells are stacked in series.
Amp-hours (Ah) and watt-hours (Wh) quantify capacity and energy:
Amp-hour definition:
1\ \text{Ah} = 1\ \text{A} \cdot 1\ \text{h} = 3600\ \text{s} \cdot 1\ \text{A} = 3600\ \text{C}.Watt-hour definition:
\text{Wh} = \text{V} \cdot \text{Ah}.
Example: a small AA-like cell rated at $1.5\ \text{V}$ and $2.85\ \text{Ah}$ yields
E = V \cdot \text{Ah} = 1.5\ \text{V} \times 2.85\ \text{Ah} = 4.275\ \text{Wh},
which equals about 4.275\ \text{Wh} \times 3600 \text{ J/Wh} \approx 15{,}390\ \text{J}.Another example from the lecture: if a cell has charge $Q = 10{,}260\ \text{C}$ and voltage $V = 1.5\ \text{V}$, then
E = Q \cdot V = 10{,}260\ \text{C} \times 1.5\ \text{V} \approx 15{,}390\ \text{J}.Parallel vs series configurations:
Series: total voltage adds up,
V{\text{series}} = \sumi Vi;\quad E{\text{series}} = \sumi Ei.Parallel: voltage stays the same as a single cell, but energy/current capacity increases, effectively increasing total capacity by the number of cells in parallel.
In a practical pack, adding cells in series increases voltage; adding cells in parallel increases capacity and current capability.
In a longer chain (series) of batteries, a single weak cell can degrade the entire string (increased effective resistance; reduced overall current under load).
Unloaded battery readings can be misleading; a battery can appear good when not under load, but its performance under load reveals actual health.
The charging/discharging cycles and internal resistance evolve with age, affecting the overall performance of a pack.
A practical note: the ability to detect true capacity requires testing under load, not just an open-circuit voltage reading.
Real-world and practical battery types; charging, aging, and ratings
Primary (non-rechargeable) vs secondary (rechargeable) chemistries:
Lead-acid is a common rechargeable chemistry; typical per-cell voltage is about V_{cell} \approx 2\ \text{V}. A 12 V lead-acid battery contains about 6 cells in series (≈12 V).
Lead-acid variants include gel and marine batteries; other forms include flooded (wet) lead-acid.
Common rechargeable chemistries:
NiMH (nickel-metal hydride): ~1.2 V per cell; often used in AA/AAA sizes as rechargeable equivalents to NiCd.
NiCd (nickel-cadmium): ~1.2 V per cell; older technology with memory effects; less common today.
Li-ion / Li-Poly (lithium) chemistries: nominal voltages around 3.6–3.7 V per cell; very high energy density per weight; expensive; long shelf life; chemistry and form factor vary widely.
Lithium also includes oxide-based chemistries (e.g., LiCoO2, LiMn2O4) with high energy densities.
The voltage of a battery pack does not scale simply with size; it scales with the number of cells in series and the chemistry of each cell.
Energy vs. weight: lithium-based cells have high energy density (energy per weight), contributing to longer runtimes for smaller, lighter packs compared to lead-acid or NiMH.
Battery ratings and terms:
Amp-hours (Ah): capacity rating that indicates how long a battery can deliver a given current before discharge, under specified conditions.
Milliamp-hours (mAh): 1 Ah = 1000 mAh; often used for smaller consumer batteries.
Watt-hours (Wh): energy capacity measure; ext{Wh} = \text{V} \cdot \text{Ah}.
Example calculations:
A Li-ion cell with 3.7 V and 1.5 Ah has energy E = 3.7\ \text{V} \times 1.5\ \text{Ah} = 5.55\ \text{Wh}.
Converting to joules: 1\ \text{Wh} = 3600\ \text{J},\quad E = 5.55\ \text{Wh} \times 3600\ \text{J/Wh} \approx 19980\ \text{J}.
Series battery health: all cells in a series must be healthy and balanced; a single degraded cell raises the series resistance and reduces output voltage under load.
The “memory effect” and charging behavior: some chemistries (e.g., certain NiCd families) historically showed memory effects; modern Li-ion/NiMH have different aging and memory characteristics. The lecturer describes a hypothetical memory effect where charging could become self-accelerating or infinite without remembering prior charge states; real systems do not behave that way, but it highlights that charging history and cycle life matter.
Practical notes on testing and usage:
Unloaded readings can be deceptive; always test under load to assess real capacity.
Under extreme use, internal resistance increases and capacity degrades.
Historical/corrosion context:
Copper corrosion in the Statue of Liberty case study illustrates how dissimilar metals exposed to electrolytes in contact can experience galvanic corrosion.
A protective layer (shellac, then PTFE insulation) and sacrificial anodes are used in marine environments to prevent metal loss and damage.
Battery applications and design trade-offs:
The choice of chemistry balances voltage per cell, energy density (Wh/kg), power density (W/kg), cycle life, cost, and safety.
For high-drain devices, high energy density and robust current capability are desirable (e.g., Li-ion in consumer electronics); for inexpensive, heavy-duty applications, lead-acid may be favored.
Final practical takeaway: battery design involves balancing chemistry, cell count, configuration (series/parallel), capacity ratings (Ah, Wh), and real-world performance under load, aging, and temperature effects.
Summary of key relationships and formulas
Series current in a simple circuit: current is the same through all elements; total voltage is the sum of individual voltages when cells are in series.
Ohm’s law in a single-resistor example:
I = \frac{V}{R}.Redox cell potential (example copper–zinc):
E{\text{cell}} = E^\circ{\text{cathode}} - E^\circ_{\text{anode}} \approx 0.34 - (-0.76) \approx 1.10\ \text{V}.Battery configurations:
Series: V{\text{series}} = \sumi Vi,\quad E{\text{series}} = \sumi Ei.
Parallel: V{\text{parallel}} = Vi,\quad E{\text{parallel}} = n Ei\; (\text{for } n \text{ cells in parallel}).
Capacity and energy:
1\ \text{Ah} = 1\ \text{A} \cdot 1\ \text{h} = 3600\ \text{s} \cdot 1\ \text{A} = 3600\ \text{C}.
\text{Wh} = \text{V} \cdot \text{Ah}.
For charge-based energy: E = q \cdot V = (I t) V.
Example charge-to-energy conversion:
If $Q = 10{,}260\ \text{C}$ and $V = 1.5\ \text{V}$, then
E = Q V = 10{,}260\ \text{C} \times 1.5\ \text{V} \approx 15{,}390\ \text{J}.
Battery names and scales:
A single 1.5 V cell (e.g., AA) vs a multi-cell 9 V configuration; the latter achieves higher voltage via stacking.
Lithium-based cells have high energy density but higher cost; lead-acid is cheaper and heavier with shorter cycle life.
Notable real-world examples and anecdotes from the lecture
Statue of Liberty copper skin corrosion: the copper skin and copper saddles with iron mounts led to corrosion between dissimilar metals; required replacing copper straps and insulating layers to prevent breakdown.
Boats in saltwater: galvanic corrosion occurs where brass propellers interact with aluminum or steel hulls; sacrificial anodes are used to protect the more noble metals by sacrificing themselves.
A practical reminder: discharge under load to assess capacity; unloaded voltages can mislead about the true health of a battery.
The most important parts of these notes cover fundamental concepts in circuits and batteries, including:
Circuit Current Limits: Understanding how to calculate maximum current in a circuit using Ohm's Law (I = \frac{V}{R}) and how it affects voltage stability.
Cell vs. Battery Definition: Differentiating between a single electrochemical cell and a battery (a collection of cells), and recognizing that voltage is determined by cell chemistry and the number of cells in series, not physical size.
Redox Reactions: Grasping the principles of reduction-oxidation reactions in electrochemical cells, specifically how electrons flow from anode (oxidation) to cathode (reduction), and how cell potential (E{\text{cell}} from $E^\circ{\text{cathode}} - E^\circ_{\text{anode}}) is derived from electrode potentials.
Battery Capacity and Energy: Knowing the definitions of Amp-hours (Ah) for capacity (1\text{ Ah} = 3600\text{ C}) and Watt-hours (Wh) for energy (\text{Wh} = \text{V} \cdot \text{Ah}$$). Understanding how series and parallel configurations impact total voltage or capacity, and the critical point that a single weak cell can compromise an entire series string.
Battery Chemistries and Real-world Performance: Being familiar with different primary and secondary battery chemistries (e.g., Lead-acid, NiMH, Li-ion), their nominal voltages, and the concept of energy density. It's crucial to understand that a battery's true health and capacity should always be assessed under load, as unloaded readings can be misleading.
Galvanic Corrosion: Recognizing real-world examples of galvanic corrosion (like the Statue of Liberty and marine environments) and how dissimilar metals in an electrolyte can lead to electrochemical wear.
In essence, the notes aim to provide a foundational understanding of how circuits behave under current, the electrochemical principles governing batteries, how batteries are configured and rated, and practical considerations for their use and longevity.