Why terminal potential difference of A battery decreases as current increases?
2 Answers
The terminal potential difference (or terminal voltage) of a battery decreases as the current drawn from the battery increases due to internal resistance. Here’s a detailed explanation of why this happens:
### 1. **Understanding Terminal Potential Difference**
The terminal potential difference of a battery is the voltage you measure across its terminals when it is connected to a load. This voltage is influenced by the internal characteristics of the battery and the current flowing through it.
### 2. **Internal Resistance of a Battery**
Every battery has a certain amount of internal resistance, denoted as \( r_{\text{int}} \). This resistance is due to the materials and chemical processes inside the battery. It affects how the battery performs under different loads.
### 3. **Ohm’s Law and Battery Voltage**
According to Ohm’s Law, the total voltage (\( V \)) of a battery is the sum of the terminal potential difference (\( V_{\text{terminal}} \)) and the voltage drop across the internal resistance. This can be expressed as:
\[ V = V_{\text{terminal}} + I \cdot r_{\text{int}} \]
Where:
- \( V \) is the electromotive force (EMF) of the battery (the voltage when no current is flowing).
- \( I \) is the current flowing through the battery.
- \( r_{\text{int}} \) is the internal resistance of the battery.
### 4. **Effect of Increasing Current**
When the current drawn from the battery increases, the voltage drop across the internal resistance also increases. This drop is given by \( I \cdot r_{\text{int}} \). The terminal potential difference is therefore given by:
\[ V_{\text{terminal}} = V - I \cdot r_{\text{int}} \]
As the current \( I \) increases, \( I \cdot r_{\text{int}} \) becomes larger, which reduces the terminal potential difference \( V_{\text{terminal}} \).
### 5. **Why Does Internal Resistance Cause This?**
Internal resistance causes this effect because it represents a form of energy loss within the battery. As current flows through the battery, energy is dissipated as heat due to the internal resistance. This reduces the amount of energy available to appear as voltage across the terminals.
### 6. **Illustrative Example**
Imagine a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If no current is drawn, the terminal potential difference is equal to the EMF, which is 12 volts. If you connect a load that draws a current of 2 amps, the voltage drop across the internal resistance would be:
\[ \text{Voltage drop} = I \cdot r_{\text{int}} = 2 \, \text{amps} \cdot 1 \, \text{ohm} = 2 \, \text{volts} \]
Thus, the terminal potential difference would be:
\[ V_{\text{terminal}} = V - \text{Voltage drop} = 12 \, \text{volts} - 2 \, \text{volts} = 10 \, \text{volts} \]
If the current increases to 4 amps, the voltage drop becomes:
\[ \text{Voltage drop} = 4 \, \text{amps} \cdot 1 \, \text{ohm} = 4 \, \text{volts} \]
The terminal potential difference now is:
\[ V_{\text{terminal}} = 12 \, \text{volts} - 4 \, \text{volts} = 8 \, \text{volts} \]
### 7. **Summary**
In summary, the terminal potential difference of a battery decreases as the current increases due to the voltage drop across the battery’s internal resistance. This internal resistance causes part of the battery’s total voltage to be used up in overcoming the resistance inside the battery, leading to a lower voltage available at the terminals when a higher current is drawn.
### 1. **Understanding Terminal Potential Difference**
The terminal potential difference of a battery is the voltage you measure across its terminals when it is connected to a load. This voltage is influenced by the internal characteristics of the battery and the current flowing through it.
### 2. **Internal Resistance of a Battery**
Every battery has a certain amount of internal resistance, denoted as \( r_{\text{int}} \). This resistance is due to the materials and chemical processes inside the battery. It affects how the battery performs under different loads.
### 3. **Ohm’s Law and Battery Voltage**
According to Ohm’s Law, the total voltage (\( V \)) of a battery is the sum of the terminal potential difference (\( V_{\text{terminal}} \)) and the voltage drop across the internal resistance. This can be expressed as:
\[ V = V_{\text{terminal}} + I \cdot r_{\text{int}} \]
Where:
- \( V \) is the electromotive force (EMF) of the battery (the voltage when no current is flowing).
- \( I \) is the current flowing through the battery.
- \( r_{\text{int}} \) is the internal resistance of the battery.
### 4. **Effect of Increasing Current**
When the current drawn from the battery increases, the voltage drop across the internal resistance also increases. This drop is given by \( I \cdot r_{\text{int}} \). The terminal potential difference is therefore given by:
\[ V_{\text{terminal}} = V - I \cdot r_{\text{int}} \]
As the current \( I \) increases, \( I \cdot r_{\text{int}} \) becomes larger, which reduces the terminal potential difference \( V_{\text{terminal}} \).
### 5. **Why Does Internal Resistance Cause This?**
Internal resistance causes this effect because it represents a form of energy loss within the battery. As current flows through the battery, energy is dissipated as heat due to the internal resistance. This reduces the amount of energy available to appear as voltage across the terminals.
### 6. **Illustrative Example**
Imagine a battery with an EMF of 12 volts and an internal resistance of 1 ohm. If no current is drawn, the terminal potential difference is equal to the EMF, which is 12 volts. If you connect a load that draws a current of 2 amps, the voltage drop across the internal resistance would be:
\[ \text{Voltage drop} = I \cdot r_{\text{int}} = 2 \, \text{amps} \cdot 1 \, \text{ohm} = 2 \, \text{volts} \]
Thus, the terminal potential difference would be:
\[ V_{\text{terminal}} = V - \text{Voltage drop} = 12 \, \text{volts} - 2 \, \text{volts} = 10 \, \text{volts} \]
If the current increases to 4 amps, the voltage drop becomes:
\[ \text{Voltage drop} = 4 \, \text{amps} \cdot 1 \, \text{ohm} = 4 \, \text{volts} \]
The terminal potential difference now is:
\[ V_{\text{terminal}} = 12 \, \text{volts} - 4 \, \text{volts} = 8 \, \text{volts} \]
### 7. **Summary**
In summary, the terminal potential difference of a battery decreases as the current increases due to the voltage drop across the battery’s internal resistance. This internal resistance causes part of the battery’s total voltage to be used up in overcoming the resistance inside the battery, leading to a lower voltage available at the terminals when a higher current is drawn.