The relative compaction R_c is related to the void ratio of soil by _______
a) \(\frac{(1+e)}{(1+e_{max})}\)
b) \(\frac{(1+e)}{(1+e_{min})}\)
c) \(\frac{(1+e_{min})}{(1+e)}\)
d) \(\frac{(1+e_{max})}{(1+e_{min})}\)

Answer: c
Explanation: The relative compaction is given by,
\(R_c = \frac{γ_d}{γ_{d,max}}\)
Since γ_d=γ_s(1+e_min)
γ_d,max=γ_s(1+e)
\(R_c= \frac{γ_d}{γ_{d,max}}= \frac{γ_s(1+e_{min})}{γ_s(1+e)} \)
\(R_c= \frac{(1+e_{min})}{(1+e)}. \)