SOLUTION

The given circuit contains a 15V source, a 4kΩ resistor, and a 6V Zener diode in parallel with a variable resistor R. The task is to find the minimum value of R that will turn on the Zener diode.

Here’s how we can approach this problem:

Zener Diode Behavior:

• A Zener diode acts like a voltage regulator when it is reverse-biased and the voltage across it exceeds its breakdown voltage.
• Zener diode can be turned ON (conducts current) only if the voltage drop across it is equal to or greater than its Zener breakdown voltage.
• In this case, the Zener diode will start conducting when the voltage across it reaches 6V.

Circuit Analysis:

• To ensure that the Zener diode conducts, the voltage across it must be at least 6V.
• Since the Zener diode and resistor R are in parallel, they will have the same voltage across them.
• Therefore, we need to find the minimum value of R that will allow a 6V drop across it.

Calculating the Current:

• The total current flowing through the 4kΩ resistor and the Zener diode will be the same.
• We can calculate the current using Ohm’s law:
• I = (15V – 6V) / 4kΩ = 2.25 mA

Calculating the Minimum Value of R:

• Now that we know the current through R, we can use Ohm’s law again to find the minimum value of R:
• R = 6V / 2.25 mA = 2.67 kΩ

Therefore, the minimum value of R that will turn on the Zener diode is 2.67 kΩ.