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Why is terminal voltage sometimes less than the expected voltage of a battery?

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The terminal voltage of a battery can be less than the expected voltage due to several factors. Here’s a detailed explanation:

### 1. **Internal Resistance**
   - **Description**: All batteries have internal resistance, which impedes the flow of current within the battery. When a battery is under load (i.e., when it is powering a device), this internal resistance causes a voltage drop inside the battery.
   - **Impact**: The greater the current drawn, the larger the voltage drop across the internal resistance, and hence, the terminal voltage (the voltage available at the battery terminals) will be lower than the nominal (or expected) voltage.

### 2. **State of Charge (SOC)**
   - **Description**: A battery’s terminal voltage is directly related to its state of charge. As a battery discharges, its terminal voltage decreases.
   - **Impact**: When a battery is nearly depleted, its terminal voltage will be significantly lower than when it is fully charged. This voltage drop is more pronounced under load.

### 3. **Load Current**
   - **Description**: The current drawn by the load affects the terminal voltage. High current draws cause a greater voltage drop across the internal resistance of the battery.
   - **Impact**: If a battery is designed to provide a certain voltage at a specific current, drawing more current than the design specifications can cause a significant drop in terminal voltage.

### 4. **Battery Chemistry**
   - **Description**: Different types of batteries (e.g., lead-acid, lithium-ion, nickel-cadmium) have different voltage characteristics and internal resistances.
   - **Impact**: Some battery chemistries exhibit more noticeable voltage drops under load due to their inherent properties.

### 5. **Temperature Effects**
   - **Description**: Battery performance, including internal resistance and voltage, can be affected by temperature. Higher temperatures can decrease internal resistance, while lower temperatures can increase it.
   - **Impact**: At low temperatures, internal resistance increases, which can cause a noticeable drop in terminal voltage under load.

### 6. **Battery Age and Condition**
   - **Description**: Over time, batteries degrade due to chemical changes and physical wear. This degradation can increase internal resistance and reduce capacity.
   - **Impact**: Older or damaged batteries may show a significant drop in terminal voltage compared to new batteries, especially under load.

### 7. **Measurement Error**
   - **Description**: Sometimes, discrepancies in measured terminal voltage might arise from measurement inaccuracies or instrument errors.
   - **Impact**: Ensure that voltage measurements are taken correctly under similar load conditions as the expected use case.

### Summary
The terminal voltage of a battery can be lower than its expected nominal voltage due to factors like internal resistance, state of charge, load current, battery chemistry, temperature, age, and measurement errors. Each of these factors can contribute to the difference between the expected and actual terminal voltage.
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