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 ___ Ω.

We need to find the protective resistance in a Zener diode voltage regulating circuit.

Zener breakdown voltage: $$V_Z = 10$$ V

Maximum power dissipation of Zener: $$P_{max} = 0.4$$ W

Supply voltage: $$V_S = 15$$ V

$$I_Z = \frac{P_{max}}{V_Z} = \frac{0.4}{10} = 0.04 \text{ A} = 40 \text{ mA}$$

The voltage drop across the protective resistance:

$$V_R = V_S - V_Z = 15 - 10 = 5 \text{ V}$$

The protective resistance must limit the current through the Zener to its maximum value (assuming no load current, worst case):

$$R = \frac{V_R}{I_Z} = \frac{5}{0.04} = 125 \, \Omega$$

Therefore, the approximate value of the protective resistance is 125 ohm.