A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The approximate value of protective resistance in this circuit is $\_\_\_\_$ $\Omega$.

The maximum current through the Zener diode is determined by its maximum power dissipation: $I_{Z,max} = \frac{P_{max}}{V_Z} = \frac{0.4}{10} = 0.04$ A.
The protective series resistance must limit the current such that the Zener operates safely. Using Ohm's law across the series resistance and Zener when the Zener carries maximum current:
$R_s = \frac{V_{in} - V_Z}{I_{Z,max}} = \frac{15 - 10}{0.04} = \frac{5}{0.04} = 125$ Ω