Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

<p>When two conducting spheres of radii $a$ and $b$ are connected by a conducting wire, they come to the same potential because conductors in contact share charges until their potentials become equal. The potential of a charged sphere is given by $V = \frac{kQ}{R}$, where $V$ is the potential, $k$ is Coulomb's constant, $Q$ is the charge on the sphere, and $R$ is the radius of the sphere.</p> <p>For the two spheres at the same potential, we have:</p> <p>$\frac{kQ_a}{a} = \frac{kQ_b}{b}$</p> <p>Where:</p> <ul> <li>$Q_a$ and $Q_b$ are the charges on the spheres with radii $a$ and $b$, respectively.</li> <li>$k$ cancels out from both sides as it is a constant.</li> </ul> <p>From the above equation, to find the ratio of charges $\frac{Q_a}{Q_b}$, we rearrange it as follows:</p> <p>$\frac{Q_a}{Q_b} = \frac{a}{b}$</p> <p>Therefore, the ratio of the charges of the two spheres respectively is $\frac{a}{b}$.</p> <p>So, the correct answer is Option C: $\frac{a}{b}$. </p>