**Core Concept**
The concept of safe yield of water refers to the maximum sustainable rate at which groundwater can be extracted from an aquifer without causing a decline in the water table or depleting the aquifer's storage capacity. This is a critical consideration in the management of groundwater resources, particularly in areas where the aquifer is the primary source of drinking water.

**Why the Correct Answer is Right**
The safe yield of a water-bearing aquifer is determined by the recharge rate of the aquifer, which is the rate at which water is added to the aquifer through natural processes such as precipitation and surface water infiltration. If the rate of groundwater extraction exceeds the recharge rate, the water table will decline, and the aquifer's storage capacity will be depleted. This can lead to a range of negative consequences, including decreased water levels, land subsidence, and contamination of the aquifer with surface water or other pollutants.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because safe yield is not solely determined by the aquifer's transmissivity, although this is an important factor.
**Option B:** Incorrect because safe yield is not solely determined by the aquifer's storage capacity, although this is a critical consideration.
**Option C:** Incorrect because safe yield is not solely determined by the recharge rate, although this is a key factor in determining the aquifer's sustainability.

**Clinical Pearl / High-Yield Fact**
A key consideration in determining the safe yield of a water-bearing aquifer is the concept of "pumping-induced stress," which refers to the decline in water levels and decrease in aquifer storage capacity that occurs when groundwater is extracted at a rate that exceeds the recharge rate.

**Correct Answer: C. Recharge rate.