The resistances of individual sections $r_1, r_2, r_3, \dots, r_n$ decrease in a geometric progression.

$\alpha$ is the ratio of minimum starting current ($I_{min}$) to maximum starting current ($I_{max}$), where $\alpha < 1$.

$R_n$ represents the total circuit resistance when the stud is on the $n$-th step.

Ensures equal upper current limits ($I_{max}$) and lower current limits ($I_{min}$) during each step of starting.

Provides smooth acceleration of the DC motor without excessive current spikes.

Requires precise calculation of non-uniform resistance steps.

Power loss occurs across the external resistance during the starting phase.

Design of multi-step resistance starters for DC shunt and series motors.

Rotor resistance starters for 3-phase slip ring induction motors.

Option A is correct because $r_n$ is directly defined as the difference between the total circuit resistance at step $n$ ($R_n$) and step $n+1$ ($R_{n+1}$).

Option B and Option C are correct because section resistances decrease in GP with common ratio $\alpha$, so $r_n = \alpha r_{n-1} = \alpha^{n-1} r_1$.

Hence, Option D ('All of these') is the correct choice.