Understanding the behavior of a battery in a circuit is crucial in physics. When a battery supplies current to an external circuit, its terminal potential difference is usually less than its electromotive force (EMF) due to the voltage drop across its internal resistance. This problem asks us to calculate the terminal potential difference for a given battery connected to a resistor.

Battery Circuit Analysis: Key Concepts

• Electromotive Force (EMF): The EMF of a battery, denoted by \(E\), is the maximum potential difference it can provide when no current is flowing through it (i.e., in an open circuit). It represents the energy supplied by the battery per unit charge.
• Internal Resistance: Every real battery has some internal resistance, denoted by \(r\). This resistance is inherent to the materials inside the battery and causes a voltage drop when current flows.
• External Resistance: The resistor connected to the battery in the circuit is called the external resistance, denoted by \(R\).
• Terminal Potential Difference: The terminal potential difference (\(V\)) is the actual voltage available across the terminals of the battery when it is supplying current to the external circuit. It is also the potential difference across the external resistor.

Calculating Terminal Potential Difference

To find the terminal potential difference of the battery, we first need to determine the total current flowing through the circuit. The total resistance in the circuit is the sum of the external resistance and the internal resistance of the battery.

Given values:

Current Calculation in the Circuit

The total equivalent resistance of the circuit when the battery is connected to the resistor is the sum of the external resistance and the internal resistance:

$$R_{\text{total}} = R + r$$

Substitute the given values:

$$R_{\text{total}} = 11 \, \Omega + 1.0 \, \Omega = 12 \, \Omega$$

Using Ohm's law, the total current (\(I\)) flowing through the circuit is given by the formula:

$$I = \frac{E}{R_{\text{total}}}$$

Substitute the values for EMF and total resistance:

$$I = \frac{6.0 \text{ V}}{12 \, \Omega} = 0.5 \text{ A}$$

Terminal Potential Difference Calculation

The terminal potential difference (\(V\)) across the battery can be calculated using the formula that accounts for the voltage drop across the internal resistance:

$$V = E - Ir$$

This formula subtracts the voltage drop across the internal resistance (\(Ir\)) from the total EMF of the battery. Substituting the calculated current and given values:

$$V = 6.0 \text{ V} - (0.5 \text{ A} \times 1.0 \, \Omega)$$

$$V = 6.0 \text{ V} - 0.5 \text{ V}$$

$$V = 5.5 \text{ V}$$

Alternatively, the terminal potential difference is also the voltage drop across the external resistor, which can be found using Ohm's law:

$$V = IR$$

Substituting the current and external resistance:

$$V = 0.5 \text{ A} \times 11 \, \Omega$$

$$V = 5.5 \text{ V}$$

Both methods yield the same result, confirming the calculation for the terminal potential difference.

Therefore, the terminal potential difference for the battery is \(5.5 \text{ V}\).