Why terminal potential difference of a battery decreases as current increases?
2 Answers
The terminal potential difference (or voltage) of a battery decreases as current increases due to the internal resistance of the battery. Here's a detailed explanation of why this happens:
### Battery Basics
A battery consists of one or more electrochemical cells that convert chemical energy into electrical energy. The battery has two key properties:
1. **Electromotive Force (EMF):** This is the maximum potential difference the battery can provide when no current is flowing (open circuit).
2. **Internal Resistance (r):** This is the resistance within the battery itself, caused by the materials and the chemical processes inside it.
### Understanding Terminal Potential Difference
When a battery is connected to an external circuit and current flows, the terminal potential difference (V_terminal) is the voltage measured across the battery terminals. It’s affected by both the EMF of the battery and the internal resistance.
### Ohm’s Law and Internal Resistance
The relationship between the EMF (E), terminal potential difference (V_terminal), internal resistance (r), and the current (I) flowing through the circuit can be described by the following equation:
\[ V_{\text{terminal}} = E - I \cdot r \]
Here's how this works in practice:
1. **When No Current Flows:** If the circuit is open and no current flows, the terminal potential difference is equal to the EMF of the battery.
2. **When Current Flows:** As current starts to flow through the battery, it encounters the internal resistance. According to Ohm's Law, the voltage drop due to the internal resistance is given by \( I \cdot r \), where \( I \) is the current and \( r \) is the internal resistance.
3. **Decrease in Terminal Potential Difference:** Because of this internal voltage drop, the terminal potential difference decreases. So, if the current increases, the voltage drop across the internal resistance increases as well, causing a greater reduction in the terminal voltage.
### Practical Example
Consider a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If no current is flowing, the terminal voltage is 12 volts.
- **If a small current of 1 ampere flows:**
\[ V_{\text{terminal}} = 12\text{V} - (1\text{A} \times 1\text{Ω}) = 11\text{V} \]
- **If a larger current of 5 amperes flows:**
\[ V_{\text{terminal}} = 12\text{V} - (5\text{A} \times 1\text{Ω}) = 7\text{V} \]
In this example, as the current increases from 1 ampere to 5 amperes, the terminal potential difference drops from 11 volts to 7 volts.
### Summary
The terminal potential difference of a battery decreases as current increases primarily due to the internal resistance of the battery. The internal resistance causes a voltage drop that increases with current, leading to a lower terminal voltage compared to the EMF when the battery is not supplying current.
### Battery Basics
A battery consists of one or more electrochemical cells that convert chemical energy into electrical energy. The battery has two key properties:
1. **Electromotive Force (EMF):** This is the maximum potential difference the battery can provide when no current is flowing (open circuit).
2. **Internal Resistance (r):** This is the resistance within the battery itself, caused by the materials and the chemical processes inside it.
### Understanding Terminal Potential Difference
When a battery is connected to an external circuit and current flows, the terminal potential difference (V_terminal) is the voltage measured across the battery terminals. It’s affected by both the EMF of the battery and the internal resistance.
### Ohm’s Law and Internal Resistance
The relationship between the EMF (E), terminal potential difference (V_terminal), internal resistance (r), and the current (I) flowing through the circuit can be described by the following equation:
\[ V_{\text{terminal}} = E - I \cdot r \]
Here's how this works in practice:
1. **When No Current Flows:** If the circuit is open and no current flows, the terminal potential difference is equal to the EMF of the battery.
2. **When Current Flows:** As current starts to flow through the battery, it encounters the internal resistance. According to Ohm's Law, the voltage drop due to the internal resistance is given by \( I \cdot r \), where \( I \) is the current and \( r \) is the internal resistance.
3. **Decrease in Terminal Potential Difference:** Because of this internal voltage drop, the terminal potential difference decreases. So, if the current increases, the voltage drop across the internal resistance increases as well, causing a greater reduction in the terminal voltage.
### Practical Example
Consider a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If no current is flowing, the terminal voltage is 12 volts.
- **If a small current of 1 ampere flows:**
\[ V_{\text{terminal}} = 12\text{V} - (1\text{A} \times 1\text{Ω}) = 11\text{V} \]
- **If a larger current of 5 amperes flows:**
\[ V_{\text{terminal}} = 12\text{V} - (5\text{A} \times 1\text{Ω}) = 7\text{V} \]
In this example, as the current increases from 1 ampere to 5 amperes, the terminal potential difference drops from 11 volts to 7 volts.
### Summary
The terminal potential difference of a battery decreases as current increases primarily due to the internal resistance of the battery. The internal resistance causes a voltage drop that increases with current, leading to a lower terminal voltage compared to the EMF when the battery is not supplying current.
The terminal potential difference (or terminal voltage) of a battery decreases as the current increases due to the internal resistance of the battery. Here’s a breakdown of why this happens:
1. **Internal Resistance**: All real batteries have some internal resistance, denoted as \( r \). This resistance causes a voltage drop within the battery when current flows through it.
2. **Ohm's Law**: According to Ohm's Law, the voltage drop across the internal resistance is given by \( V_{\text{drop}} = I \cdot r \), where \( I \) is the current and \( r \) is the internal resistance.
3. **Terminal Voltage**: The terminal voltage \( V_{\text{terminal}} \) of the battery is the voltage available across its terminals and can be expressed as:
\[
V_{\text{terminal}} = V_{\text{emf}} - I \cdot r
\]
where \( V_{\text{emf}} \) is the electromotive force (emf) of the battery (the voltage when no current flows).
4. **Current Impact**: As the current \( I \) increases, the voltage drop \( I \cdot r \) across the internal resistance becomes larger. Therefore, the terminal voltage \( V_{\text{terminal}} \) decreases because a larger portion of the emf is lost due to the internal resistance.
In summary, the more current you draw from the battery, the greater the internal voltage drop, which reduces the terminal potential difference you observe.
1. **Internal Resistance**: All real batteries have some internal resistance, denoted as \( r \). This resistance causes a voltage drop within the battery when current flows through it.
2. **Ohm's Law**: According to Ohm's Law, the voltage drop across the internal resistance is given by \( V_{\text{drop}} = I \cdot r \), where \( I \) is the current and \( r \) is the internal resistance.
3. **Terminal Voltage**: The terminal voltage \( V_{\text{terminal}} \) of the battery is the voltage available across its terminals and can be expressed as:
\[
V_{\text{terminal}} = V_{\text{emf}} - I \cdot r
\]
where \( V_{\text{emf}} \) is the electromotive force (emf) of the battery (the voltage when no current flows).
4. **Current Impact**: As the current \( I \) increases, the voltage drop \( I \cdot r \) across the internal resistance becomes larger. Therefore, the terminal voltage \( V_{\text{terminal}} \) decreases because a larger portion of the emf is lost due to the internal resistance.
In summary, the more current you draw from the battery, the greater the internal voltage drop, which reduces the terminal potential difference you observe.