An experiment is preformed to determine the `I-V` characteristics of a Zener diode, which has a protective resistance of `R = 100 Omega`, and maximum power of dissipation rating of 1 W. The minimum voltage range of the DC source in the circuit is :-

Options

A. `0-24 V`
B. `0-12 V`
C. `0-8 V`
D. `0.5 V`

Answer

To determine the minimum voltage range of the DC source in the circuit with a Zener diode, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Circuit**:
We have a Zener diode in the circuit with a protective resistance \( R = 100 \, \Omega \) and a maximum power dissipation rating of \( P = 1 \, W \).

2. **Applying Kirchhoff's Voltage Law**:
According to Kirchhoff's voltage law, the total voltage \( V \) in the circuit is the sum of the voltage drop across the resistor and the voltage drop across the Zener diode:
\[ V = I \cdot R + V_D \]
where \( I \) is the current through the circuit and \( V_D \) is the voltage across the Zener diode.

3. **Power Dissipation in the Zener Diode**:
The power dissipated in the Zener diode can be expressed as:
\[ P_Z = V_D \cdot I \]
Given that \( P_Z = 1 \, W \), we can write:
\[ 1 = V_D \cdot I \]

4. **Expressing \( V_D \)**:
Rearranging the power equation gives:
\[ V_D = \frac{1}{I} \]

5. **Substituting \( V_D \) into the Voltage Equation**:
Substituting \( V_D \) into the voltage equation, we get:
\[ V = I \cdot R + \frac{1}{I} \]
Substituting \( R = 100 \, \Omega \):
\[ V = 100I + \frac{1}{I} \]

6. **Finding the Condition for \( I \)**:
To find the minimum voltage \( V \), we need to minimize the expression \( 100I + \frac{1}{I} \). We can do this by taking the derivative and setting it to zero:
\[ \frac{dV}{dI} = 100 - \frac{1}{I^2} = 0 \]
Solving for \( I \):
\[ 100 = \frac{1}{I^2} \implies I^2 = \frac{1}{100} \implies I = \frac{1}{10} = 0.1 \, A \]

7. **Calculating Minimum Voltage \( V \)**:
Now substituting \( I = 0.1 \, A \) back into the voltage equation:
\[ V = 100 \cdot 0.1 + \frac{1}{0.1} = 10 + 10 = 20 \, V \]

8. **Conclusion**:
Therefore, the minimum voltage range of the DC source in the circuit should be greater than \( 20 \, V \). Since the options provided do not include \( 20 \, V \), we choose the next higher option which is \( 24 \, V \).

### Final Answer:
The minimum voltage range of the DC source in the circuit is \( 24 \, V \).

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