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Annex 1 (BE01) — Lesson BE.01.04 • TLO: 28XX-MAIN-1002 • ELOs: 28XX-MAIN-1002h, 28XX-MAIN-1002i

DC Power Sources

Direct current circuits rely on chemical cells and regulated DC supplies to establish a steady potential difference. Understanding cell chemistries and multi-source interconnections (Series-Aiding, Series-Opposing, and Parallel) allows a technician to predict terminal voltage, current capacity, and direction of electron flow.

1. The Voltaic Cell & Battery Classifications

The Voltaic (Galvanic) Cell

A voltaic cell converts chemical energy into electrical energy through a chemical reaction:

Electrodes (Plates): Two dissimilar conductive plates—a positive plate (electrode) and a negative plate (electrode).
Electrolyte: A conductive chemical paste or liquid acid/alkaline solution in which the electrodes are immersed. The chemical reaction between the electrolyte and electrodes accumulates excess electrons on the negative plate and a deficiency of electrons on the positive plate.
Battery Definition: A battery consists of one or more voltaic cells connected in series or parallel to achieve a desired output voltage or current rating (for example, a standard $12,\text{VDC}$ automotive battery contains six $2,\text{V}$ lead-acid cells connected in series-aiding).

Primary Cells vs. Secondary Cells

Classification	Common Name	Rechargeability	Cell Chemistry	Nominal Cell Voltage	Operational & Orientation Rules
Primary Cell	Dry Cell	Non-Rechargeable (chemical reaction cannot be reversed)	Carbon-Zinc	$1.5,\text{VDC}$	Moist paste electrolyte sealed between plates (e.g., standard AA cell); may be operated in any position.
Primary Cell	Dry Cell	Non-Rechargeable	Zinc Chloride	$1.5,\text{VDC}$	Heavy-duty dry cell; may be operated in any position.
Primary Cell	Dry Cell	Non-Rechargeable	Lithium	$3.0,\text{VDC}$	High energy density, long shelf life; may be operated in any position.
Secondary Cell	Storage / Wet Cell	Rechargeable (chemical reaction is reversible)	Nickel-Cadmium (`NiCad`)	$1.25,\text{VDC}$	Sealed wet cell; because the casing is sealed, it may be operated in any position.
Secondary Cell	Storage / Wet Cell	Rechargeable	Lead-Acid	$2.0,\text{V}$ to $2.2,\text{VDC}$	Unsealed/vented wet cell; MUST be operated and stored upright to prevent liquid electrolyte from leaking.

2. Multi-Source Battery Configurations

Multiple DC voltage sources can be interconnected in three distinct ways depending on whether the circuit requires higher voltage, reduced differential voltage, or higher current capacity.

<!-- 2. Series Opposing -->
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<!-- 3. Parallel -->
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− + − + 1.5V 1.5V 1. Series-Aiding VT = V1 + V2 = 3.0 V

<!-- Labels 2 -->
<text x="278" y="65">−</text>
<text x="313" y="60">+</text>
<text x="334" y="60">+</text>
<text x="369" y="65">−</text>
<text x="296" y="42">4.5V</text>
<text x="351" y="42">1.5V</text>
<text x="322" y="142" font-size="13">2. Series-Opposing</text>
<text x="322" y="162" font-weight="400">VT = |V1 − V2| = 3.0 V</text>

<!-- Labels 3 -->
<text x="472" y="50">+</text>
<text x="472" y="124">−</text>
<text x="546" y="85">1.5V</text>
<text x="616" y="85">1.5V</text>
<text x="555" y="142" font-size="13">3. Parallel Sources</text>
<text x="555" y="162" font-weight="400">VT = 1.5 V | IT = I1 + I2</text>

1. Series-Aiding Configuration

Physical Connection: The negative ( $-$ ) terminal of one cell is connected to the positive ( $+$ ) terminal of the next cell along a single current path.
Purpose: Used to increase total output voltage ( $V_T$ ).
Voltage Rule (Additive): $V_T = V_1 + V_2 + \dots + V_N$
Current Rule (Common / Limited by Lowest Cell): Because all series cells share a single path for current flow, current is common throughout the string. The maximum safe current capacity of the series battery is limited to the lowest current rating of any individual cell in the string.
Example: Two $1.5,\text{VDC}$ cells rated at $18,\text{mA}$ each connected in series-aiding deliver $3.0,\text{VDC}$ at $18,\text{mA}$ .

2. Series-Opposing Configuration

Physical Connection: Like-polarity terminals (positive-to-positive OR negative-to-negative) are connected together along the same series current path.
Voltage Rule (Subtractive / Difference): The opposing potentials work against one another, so net applied voltage equals the difference between the sources: $V_T = |V_1 - V_2|$ * **Equal Opposing Sources:** If two voltage sources of equal value (e.g., $9\,\text{V}$ and $9\,\text{V}$ ) are connected series-opposing, the net applied voltage is **zero ( $0\,\text{V}$ )** and no current flows.
Current Direction & Capacity: Electron flow in the circuit is dictated by the higher-voltage source (flowing out of the negative terminal of the stronger battery). Current remains common throughout the single series path.
Example: Three $1.5,\text{VDC}$ dry cells connected in series where two cells are series-aiding ( $1.5,\text{V} + 1.5,\text{V} = 3.0,\text{V}$ ) and the third cell is connected opposing ( $- 1.5,\text{V}$ ) produce a net output of $1.5,\text{VDC}$ .

3. Parallel Configuration

Physical Connection: All positive ( $+$ ) terminals are tied together and all negative ( $-$ ) terminals are tied together across separate parallel branches, with the load ( $R_L$ ) connected across the common rails.
Purpose: Used to increase total current delivery capacity ( $I_T$ ) without increasing output voltage.
Voltage Rule (Common): All parallel cells must have the same nominal voltage rating. Total output voltage equals the voltage of a single cell: $V_T = V_1 = V_2 = \dots = V_N$
Current Rule (Additive): Each parallel cell contributes its branch current to the load, so maximum current capacity is the sum of all individual cell current ratings: $I_T = I_1 + I_2 + \dots + I_N$
Example: Two $1.5,\text{VDC}$ cells rated at $500,\text{mA}$ each connected in parallel across a $100,\Omega$ load provide a source capability of $1.5,\text{VDC}$ and $1,\text{A}$ ( $500,\text{mA} + 500,\text{mA}$ ).

3. Master Comparison Matrix: DC Source Configurations

Configuration	Terminal Hookup	Current Path	Total Voltage ( $V_T$ )	Max Current Capacity ( $I_T$ )	Primary Engineering Application
Series-Aiding	Opposite terminals ( $+$ to $-$ )	Single path (Series)	Additive ( $V_1 + V_2$ )	Common (limited by lowest-rated cell)	Stepping up supply voltage (e.g., six $2,\text{V}$ cells $\rightarrow 12,\text{V}$ battery)
Series-Opposing	Like terminals ( $+$ to $+$ or $-$ to $-$ )	Single path (Series)	Difference ( $∣ V_{1} - V_{2} ∣$	V_1 - V_2	$∣ V_{1} - V_{2} ∣$ )
Parallel	Like terminals ( $+$ to $+$ and $-$ to $-$ )	Multiple branches (Parallel)	Common ( $V_T = V_1$ )	Additive ( $I_1 + I_2 + \dots$ )	Increasing amperage / amp-hour runtime at constant voltage

4. Bench & Troubleshooting Application (`BE.01.04` Lab)

In the BE.01.04 practical laboratory, students combine the $5,\text{VDC}$ regulated breadboard supply ( $V_1$ ) with an external $9,\text{VDC}$ battery ( $V_2$ ) across a $5,\text{k}\Omega$ load resistor ( $R_1$ ):

1. Verifying Series-Aiding on the Breadboard

Wiring: Connect the negative rail of the $5,\text{VDC}$ breadboard supply to circuit ground, connect the positive output of the $5,\text{VDC}$ supply to the negative (black) snap lead of the $9,\text{VDC}$ battery in an isolated breadboard row, and route the positive (red) snap lead of the $9,\text{VDC}$ battery through the $5,\text{k}\Omega$ load resistor back to ground.
Expected Telemetry:
- Across $V_1$ : $\approx 5.00,\text{VDC}$
- Across $V_2$ : $\approx 9.00,\text{VDC}$
- Across Load $R_1$ ( $V_T = V_1 + V_2$ ): $\approx 14.00,\text{VDC}$

2. Verifying Series-Opposing on the Breadboard

Wiring: Reverse the $9,\text{VDC}$ battery leads so that the positive ( $+$ ) terminal of the $5,\text{VDC}$ breadboard supply connects to the positive (red) snap lead of the $9,\text{VDC}$ battery in series with the $5,\text{k}\Omega$ resistor.
Expected Telemetry:
- Across $V_1$ : $\approx 5.00,\text{VDC}$
- Across $V_2$ : $\approx 9.00,\text{VDC}$
- Across Load $R_1$ ( $V_T = |9,\text{V} - 5,\text{V}|$ ): $\approx 4.00,\text{VDC}$ (with polarity driven by the stronger $9,\text{V}$ battery).

3. Why Unequal Sources Are Never Wired Directly in Parallel

Never wire the $9,\text{V}$ battery directly in parallel with the $5,\text{V}$ breadboard supply. Because parallel branches share a common voltage node, connecting a $9,\text{V}$ source directly across a $5,\text{V}$ source forces high circulating current from the $9,\text{V}$ battery backward into the $5,\text{V}$ regulator, overheating the battery and potentially damaging the breadboard regulator. In the BE.01.04 lab, parallel voltage commonality is demonstrated instead by placing parallel resistive branches ( $1,\text{k}\Omega \parallel 10,\text{k}\Omega$ ) across the single $5,\text{V}$ source.

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