When the emf of a battery is equal to its terminal potential difference?
2 Answers
When the electromotive force (emf) of a battery is equal to its terminal potential difference, it typically occurs under open-circuit conditions, meaning no current is flowing through the battery. In this state, the voltage measured across the terminals is equal to the battery's emf because there are no internal voltage drops due to resistance within the battery itself. This scenario represents the ultimate condition for measuring a battery's potential, as any current draw would lead to a voltage drop, resulting in a lower terminal potential difference. Would you like to delve into the implications of this in a circuit?
The electromotive force (EMF) of a battery is a measure of the maximum potential difference the battery can provide when no current is flowing through the circuit. The terminal potential difference, on the other hand, is the voltage across the terminals of the battery when it is connected in a circuit and current is flowing.
The EMF of a battery is equal to its terminal potential difference in a specific condition:
### **When the Battery is Not Delivering Current**
1. **No Load Condition**: When the battery is not connected to any external circuit (or the circuit is open), there is no current flowing through the battery. In this condition, the terminal potential difference is equal to the EMF of the battery because there are no voltage drops across any internal resistance.
2. **Internal Resistance**: The internal resistance of a battery causes a voltage drop when current flows through it. This internal resistance (denoted as \( r \)) is a key factor in determining the terminal potential difference. According to Ohm's law and the definition of EMF, the relationship can be described as:
\[
V_{\text{terminal}} = \text{EMF} - I \cdot r
\]
where \( I \) is the current flowing through the circuit, and \( r \) is the internal resistance of the battery.
When there is no current (\( I = 0 \)), the equation simplifies to:
\[
V_{\text{terminal}} = \text{EMF} - 0 \cdot r = \text{EMF}
\]
### **Summary**
The EMF of a battery equals its terminal potential difference when the battery is not providing any current to the circuit. This situation occurs when there is an open circuit or when no load is connected, meaning no current is flowing through the battery’s internal resistance.
The EMF of a battery is equal to its terminal potential difference in a specific condition:
### **When the Battery is Not Delivering Current**
1. **No Load Condition**: When the battery is not connected to any external circuit (or the circuit is open), there is no current flowing through the battery. In this condition, the terminal potential difference is equal to the EMF of the battery because there are no voltage drops across any internal resistance.
2. **Internal Resistance**: The internal resistance of a battery causes a voltage drop when current flows through it. This internal resistance (denoted as \( r \)) is a key factor in determining the terminal potential difference. According to Ohm's law and the definition of EMF, the relationship can be described as:
\[
V_{\text{terminal}} = \text{EMF} - I \cdot r
\]
where \( I \) is the current flowing through the circuit, and \( r \) is the internal resistance of the battery.
When there is no current (\( I = 0 \)), the equation simplifies to:
\[
V_{\text{terminal}} = \text{EMF} - 0 \cdot r = \text{EMF}
\]
### **Summary**
The EMF of a battery equals its terminal potential difference when the battery is not providing any current to the circuit. This situation occurs when there is an open circuit or when no load is connected, meaning no current is flowing through the battery’s internal resistance.