The maximum resistance which can be made using four resistors each of resistance $\frac{1}{2} \Omega$ is

<strong>Why the key is correct:</strong> To obtain the maximum possible resistance from a given set of resistors, they must be connected in series. In a series combination, the equivalent resistance $R_s$ is the sum of individual resistances: $$R_s = R_1 + R_2 + R_3 + R_4$$ Here, we have four resistors, each of resistance $R = \frac{1}{2}\ \Omega$. Therefore: $$R_s = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 2\ \Omega$$<br><strong>Why distractors are incorrect:</strong><ul><li><strong>Option B ($1\ \Omega$):</strong> This value is obtained if only two of the resistors are connected in series, or if a different combination is used, but it is not the maximum possible resistance.</li><li><strong>Option C ($2.5\ \Omega$):</strong> This value is greater than the maximum possible resistance of $2\ \Omega$ that can be formed by these four resistors.</li><li><strong>Option D ($8\ \Omega$):</strong> This value is incorrect and would require much larger individual resistances (e.g., four $2\ \Omega$ resistors in series).</li></ul>