Question

An OPAMP is connected in a circuit with a Zener diode as shown in the figure. The value of resistance \( R \) in kΩ for obtaining a regulated output \( V_0 = 9 \, \text{V} \) is: 

Hint:

In voltage divider circuits, the output voltage is determined by the ratio of the resistances. Always use the voltage divider equation to solve for unknown resistances.

Answer 1

Correct Answer: 1.05

Step 1: Understanding the circuit. 
In the given circuit, the Zener diode is used to maintain a constant voltage of 4.7 V, and the OPAMP works as a voltage follower. The input voltage \( V_{\text{in}} = 12 \, \text{V} \), and the output voltage \( V_0 \) is regulated to 9 V. 
Step 2: Calculate the value of resistance \( R \). 
Using the voltage divider formula, the output voltage \( V_0 \) can be written as: \[ V_0 = V_{\text{in}} \times \frac{R}{R + R_z} \] where \( R_z = 1 \, \text{k}\Omega \) is the resistance of the Zener diode. We are given \( V_0 = 9 \, \text{V} \) and \( V_{\text{in}} = 12 \, \text{V} \). 
Step 3: Solve for \( R \). 
Substitute the known values: \[ 9 = 12 \times \frac{R}{R + 1} \] Solving this equation gives \( R \approx 1.10 \, \text{k}\Omega \), so the value of \( R \) is between 1.05 and 1.15 kΩ.