To find the maximum current through the Zener diode, we first need to understand the circuit provided. We have a Zener diode with a breakdown voltage of 10 \, V, a series resistor of 820 \, \Omega, and a variable supply voltage ranging from 20 \, V to 40 \, V.

Step-by-step calculation:

1. The Zener diode will start conducting when the supply voltage exceeds the breakdown voltage of 10 \, V. Therefore, the Zener maintains a constant output voltage of 10 \, V.
2. To find the maximum current through the Zener diode, use the maximum supply voltage, which is 40 \, V.
3. Apply Kirchhoff’s Voltage Law (KVL) around the loop: V_{supply} = V_{R} + V_{Z} where V_{supply} = 40 \, V and V_{Z} = 10 \, V.
4. Calculate the voltage across the series resistor (V_{R}): V_{R} = V_{supply} - V_{Z} = 40 \, V - 10 \, V = 30 \, V.
5. Use Ohm's Law to find the current (I_{Z}) through the Zener diode: I_{Z} = \frac{V_{R}}{R} = \frac{30 \, V}{820 \, \Omega} \approx 36.6 \, mA.

Therefore, the maximum current through the Zener diode is 36.6 \, mA, matching option B.