A Zener diode voltage regulator circuit is connected to an unregulated DC input voltage of 24 V . The circuit uses a series resistor of 400 and a Zener diode with a breakdown voltage of 8 V . A variable load resistor R_L is connected in parallel with the Zener diode. What is the minimum value of the load resistance R_L (in ) for which the Zener diode will maintain voltage regulation?

Step-by-step solution

For the Zener diode to maintain voltage regulation, it must be in the breakdown region. This requires the voltage across the load terminals (if the Zener were removed) to be at least equal to the Zener voltage V_z . The voltage across the load resistor without the Zener diode is given by the voltage divider rule: V_L = V_i ( R_L R_s + R_L ) At the boundary condition for regulation, V_L = V_z = 8 V . Substituting the given values: 8 = 24 ( R_L 400 + R_L ) Dividing both sides by 8 : 1 = 3 ( R_L 400 + R_L ) 400 + R_L