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To determine the current flowing through a 4.7 k ohm resistor at 13.5 volts, Ohm's Law can be applied, which states that current (I) is equal to voltage (V) divided by resistance (R). Mathematically, this is represented as:

I = V / R

Here, the voltage is given as 13.5 volts and the resistance as 4.7 k ohms. Since 4.7 k ohms is equivalent to 4700 ohms, the calculation becomes:

I = 13.5 V / 4700 Ω

Calculating this gives:

I = 0.00287 A

To convert amperes into milliamperes (mA), you multiply by 1000:

I = 0.00287 A * 1000 = 2.87 mA

This result rounds to 2.9 mA, which aligns with the option provided. Therefore, the current through the 4.7 k ohm resistor at 13.5 volts is 2.9 mA, making this the correct answer.