Since R' is connected in parallel with R and R' varies from R₀ to infinity (where R << R₀), the equivalent resistance of the parallel combination (R || R') remains slightly less than R but close to R.

1. Current I (Statement d): The total resistance of the circuit is r + (RR'/(R+R')). Since the parallel combination is always less than R, the total resistance is less than r + R. Consequently, the total current I = V / R_total will be greater than or equal to V / (r + R). Thus, statement (d) is correct.
2. Potential Drop (Statement a): The potential drop across AB is V_AB = V - Ir. Since I is determined primarily by R (as R' is large) and r is small, I is nearly constant, making V_AB nearly constant. Thus, statement (a) is correct.
3. Current through R' (Statement b): The current through R' is V_AB / R'. Since V_AB is constant and R' varies significantly, the current through R' varies inversely with R' and is not constant.