A Zener diode having a breakdown voltage $V_z = 6$ V is used in a voltage regulator circuit as shown in the figure. The minimum current required to pass through the Zener to act as a voltage regulator is $10$ mA and the maximum allowed current through the Zener is $40$ mA. The maximum value of $R_\delta$ for Zener to act as a voltage regulator is
Given: A Zener diode has a breakdown voltage of \( V_z = 6 \) V. The voltage regulator circuit passes a minimum current of \( 10 \) mA and a maximum current of \( 40 \) mA through the Zener diode. The maximum value of \( R_\delta \) for the Zener diode to act as a voltage regulator is asked.
Step 1: Understanding the Zener Regulator Circuit In a Zener diode voltage regulator circuit, the Zener diode maintains a constant voltage of \( V_z \) across it once the breakdown voltage is reached. The resistor \( R_\delta \) is used to limit the current through the diode.
Step 2: Determine the Maximum Current through the Zener The maximum current through the Zener is given as \( I_{\text{max}} = 40 \) mA, and the minimum current is \( I_{\text{min}} = 10 \) mA. We will use these values to calculate the maximum value of \( R_\delta \) such that the Zener diode operates within this range of current.
Step 3: Apply Ohm’s Law We apply Ohm's law to the circuit. The voltage drop across the resistor \( R_\delta \) will be: \[ V_R = V_{\text{in}} - V_z \] where \( V_{\text{in}} \) is the input voltage. The current through the resistor \( R_\delta \) is: \[ I_R = I_{\text{max}} = 40 \text{ mA}. \] So, the maximum value of \( R_\delta \) is: \[ R_\delta = \frac{V_R}{I_R} = \frac{V_{\text{in}} - V_z}{I_{\text{max}}}. \]
Step 4: Calculate the Maximum Resistance We know that the minimum current is \( 10 \) mA, and the maximum current is \( 40 \) mA. The Zener diode operates in the breakdown region if the input voltage is sufficiently high. We can compute the maximum value of \( R_\delta \), keeping in mind that the maximum value of \( R_\delta \) occurs when the current is at the maximum value of \( 40 \) mA. Thus, the answer is \( \boxed{400 \, \Omega} \).
