Sum the individual voltage drops.

In a series circuit, the total voltage supplied by the battery is the sum of the voltage drops across each resistor.

$$V = V_1 + V_2 + V_3$$

Substitute the given potential differences:

$$V = 5\,V + 2\,V + 6\,V$$ $$V = \boxed{\text{13 V}}$$

The total resistance $R_{total}$ of a series circuit is the sum of individual resistances, or the total voltage divided by the total current $I$.

$$R_{total} = \frac{V}{I}$$

Substitute the total voltage from part (a):

$$R_{total} = \boxed{\frac{13\,V}{I}}$$

Since the current $I$ flowing through the circuit is not provided, the exact numerical value for the total resistance cannot be determined. It is expressed in terms of $I$.

For resistors in a series circuit, the current $I$ is the same through each resistor. Using Ohm's Law ($V = I \cdot R$):

$$R_1 = \frac{V_1}{I}$$ $$R_2 = \frac{V_2}{I}$$ $$R_3 = \frac{V_3}{I}$$

Substitute the given potential differences:

$$R_1 = \boxed{\frac{5\,V}{I}}$$ $$R_2 = \boxed{\frac{2\,V}{I}}$$ $$R_3 = \boxed{\frac{6\,V}{I}}$$

Since the current $I$ is not provided, the exact numerical values for $R_1$, $R_2$, and $R_3$ cannot be determined. They are expressed in terms of $I$.