To find the terminal voltage of the battery, we can use the formula for terminal voltage:$\\ V = \varepsilon - I \cdot r \\$Where:$\\$• $V$ is the terminal voltage.$\\$• $\varepsilon$ is the emf of the battery (10V).$\\$• $I$ is the current flowing through the circuit.$\\$• $r$ is the internal resistance of the battery (1$\Omega$).$\\$First, calculate the total resistance in the circuit:$\\ R_{total} = R_{external} + r = 4\Omega + 1\Omega = 5\Omega \\$Next, calculate the current using Ohm's Law:$\\ I = \frac{\varepsilon}{R_{total}} = \frac{10V}{5\Omega} = 2A \\$Now, substitute the values into the terminal voltage formula:$\\ V = 10V - (2A \cdot 1\Omega) \\ V = 10V - 2V \\ V = 8V \\$Therefore, the terminal voltage of the battery is $8V$. This corresponds to Option 1.