A Zener diode with a breakdown voltage of 5 V and a maximum power rating of 2 W is used in a voltage regulator circuit. The unregulated input voltage fluctuates between 8 V and 15 V . A load resistor of 50 is connected in parallel with the Zener diode. The minimum value of the series resistance required to ensure the safe operation of the Zener diode is

Step-by-step solution

The maximum safe current through the Zener diode is given by its power rating: I_ z( max ) = P_ z V_ z = 2 W 5 V = 0.4 A The current through the load resistor is constant: I_ L = V_ z R_ L = 5 V 50 = 0.1 A The total current flowing through the series resistor is the sum of the Zener current and the load current: I_ s = I_ z( max ) + I_ L = 0.4 A + 0.1 A = 0.5 A For safe operation, we must consider the worst-case scenario, which occurs when the input voltage is at its maximum ( 15 V ). The voltage drop across the se