In the Zener diode voltage regulator shown, the 7 V Zener has knee current of 5mA. What is the minimum value of RL to get regulated output voltage at V_L?

Concept:

A Zener diode regulator maintains a constant output voltage (V_Z) across the load resistor (R_L) as long as the Zener diode current is greater than or equal to its knee current (minimum operating current).

To maintain regulation, the Zener must conduct at least the knee current (I_ZK = 5 mA).

Given:

Input Voltage (V_in) = 14.5 V

Zener Voltage (V_Z) = 7 V

Series Resistance R_s = 100 Ω

Zener Knee Current I_ZK = 5 mA

Calculation:

Total current through R_s:

\( I_{total} = \frac{V_{in} - V_Z}{R_s} = \frac{14.5 - 7}{100} = 0.075~A = 75~mA \)

Minimum current required by Zener = 5 mA

So, maximum load current:

\( I_L = I_{total} - I_{ZK} = 75 - 5 = 70~mA \)

Using Ohm’s law to find minimum R_L:

\( R_L = \frac{V_Z}{I_L} = \frac{7}{0.07} = 100~\Omega \)

Final Answer:

Option 3) 100 Ω