Question

Is the potential difference across the terminals of a battery always less than its emf?

Answer 1

The potential difference across the terminals of a battery is not always less than its electromotive force (emf), but it often is in practical scenarios. Here’s a detailed explanation:

### 1. **Understanding emf and Terminal Potential Difference**

- **Electromotive Force (emf):** The emf of a battery is a measure of the maximum potential difference between the terminals of the battery when no current is flowing through the circuit. It represents the energy provided per unit charge by the battery’s chemical reaction.

- **Terminal Potential Difference:** This is the actual voltage measured across the battery terminals when the battery is connected to a circuit and current is flowing.

### 2. **Ideal vs. Real Battery**

- **Ideal Battery:** In an ideal scenario where no current flows (open circuit condition), the terminal potential difference equals the emf. There is no internal resistance, so the voltage across the terminals is simply the emf.

- **Real Battery:** In a practical battery, there is always some internal resistance. This internal resistance causes a voltage drop when current flows through the battery.

### 3. **Internal Resistance and Voltage Drop**

When current flows through the battery, the internal resistance causes a voltage drop inside the battery. This drop reduces the potential difference across the terminals compared to the emf. The relationship can be expressed as:

\[ V = \text{emf} - I \cdot r \]

where:
- \( V \) is the terminal potential difference.
- \( \text{emf} \) is the electromotive force of the battery.
- \( I \) is the current flowing through the battery.
- \( r \) is the internal resistance of the battery.

So, if the current \( I \) is greater than zero, the term \( I \cdot r \) (the internal voltage drop) is subtracted from the emf, making the terminal potential difference \( V \) less than the emf.

### 4. **Special Cases**

- **No Current (Open Circuit):** If there is no current flowing through the battery (open circuit condition), the terminal potential difference equals the emf.

- **Short Circuit:** In a short circuit (where the resistance is very low), the current is very high. The terminal potential difference can drop significantly and approach zero if the internal resistance is not negligible.

- **Low Current:** When the current is very low, the voltage drop across the internal resistance is small, and the terminal potential difference will be close to the emf.

### 5. **Summary**

- The terminal potential difference across a battery is generally less than its emf when current is flowing due to the internal resistance of the battery.
- When no current flows (in an open circuit), the terminal potential difference equals the emf.
- The difference between the emf and the terminal potential difference depends on the current flowing and the internal resistance of the battery.

In essence, while the potential difference across the terminals of a battery is often less than its emf in practical situations due to internal resistance, it can be equal to the emf when no current is flowing.

Answer 2

The potential difference across the terminals of a battery is not always less than its electromotive force (emf), but it often is, depending on the conditions. To understand why, let's break down the concepts:

### **1. Electromotive Force (emf)**
The emf of a battery is the maximum potential difference that the battery can provide when no current is flowing. It represents the energy per unit charge supplied by the battery due to the chemical reactions occurring inside it. The emf is essentially the maximum voltage the battery can produce.

### **2. Potential Difference Across the Terminals**
The potential difference across the terminals of the battery, also known as the terminal voltage, is the actual voltage you measure across the battery's terminals when it is connected to a circuit and current is flowing.

### **Factors Affecting Terminal Voltage:**

1. **Internal Resistance:**
   - **Internal Resistance (\(r\))**: All real batteries have some internal resistance due to the materials inside the battery and the design of the battery.
   - **Voltage Drop Across Internal Resistance**: When a current (\(I\)) flows through the battery, there is a voltage drop across this internal resistance, which is given by \( I \times r \). This drop reduces the terminal voltage compared to the emf.
   
   So, the terminal voltage (\(V_{\text{terminal}}\)) can be calculated as:
   \[
   V_{\text{terminal}} = \text{emf} - I \times r
   \]
   Therefore, when the battery is supplying current, the terminal voltage will be less than the emf by an amount equal to the voltage drop across the internal resistance.

2. **No Current Flow:**
   - **Open-Circuit Condition**: When no current is flowing (open-circuit condition), there is no voltage drop across the internal resistance. In this case, the terminal voltage is equal to the emf.
   
3. **High Current Flow:**
   - **Load Conditions**: If a battery is under heavy load (i.e., if a large current is drawn), the voltage drop across the internal resistance becomes significant. This will cause the terminal voltage to be considerably less than the emf.

### **In Summary:**

- **Under no-load or open-circuit conditions**: The terminal voltage equals the emf.
- **Under load conditions**: The terminal voltage is less than the emf due to the voltage drop across the internal resistance of the battery.

Understanding this helps in designing circuits and selecting appropriate batteries for different applications to ensure that the voltage delivered meets the requirements of the circuit.