A Zener diode with a breakdown voltage of 10 V is used to regulate the voltage across a variable load resistor R_L . The circuit is powered by a 30 V DC supply through a series resistor of 400 . For the Zener diode to operate in the breakdown region and act as a voltage regulator, the minimum required value of the load resistance R_L is

Step-by-step solution

For the Zener diode to operate in the breakdown region, the voltage across the load terminals (with the Zener diode considered open-circuit) must be greater than or equal to the Zener breakdown voltage V_Z . Using the voltage divider rule, the open-circuit voltage V_ oc across R_L is: V_ oc = V_ in R_L R_s + R_L Setting the condition V_ oc V_Z : 30 R_L 400 + R_L 10 Dividing both sides by 10 : 3 R_L 400 + R_L 2 R_L 400 R_L 200 Thus, the minimum required value of the load resistance is 200 . Answer: 200