In a zener regulated power supply a zener diode with
` V_z = 6.0 V` is used for regualtion. The load current is to eb 4.0 mA and the
unregulated input is 10.0 V . What should be the value of series resistor R?

Explanation

To find the value of the series resistor \( R \) in a Zener regulated power supply, we can follow these steps:

### Step 1: Identify the given values
- Zener voltage \( V_z = 6.0 \, V \)
- Load current \( I_L = 4.0 \, mA = 4.0 \times 10^{-3} \, A \)
- Unregulated input voltage \( V_{in} = 10.0 \, V \)

### Step 2: Calculate the voltage across the series resistor \( R \)
The voltage across the series resistor \( R \) can be calculated using the formula:
\[ V_R = V_{in} - V_z \]
Substituting the known values:
\[ V_R = 10.0 \, V - 6.0 \, V = 4.0 \, V \]

### Step 3: Determine the total current flowing through the resistor
The total current \( I \) flowing through the resistor \( R \) is the sum of the load current \( I_L \) and the Zener current \( I_Z \). For this calculation, we will assume the Zener current is approximately 5 times the load current (a common design practice to ensure regulation):
\[ I_Z = 5 \times I_L = 5 \times 4.0 \, mA = 20.0 \, mA = 20.0 \times 10^{-3} \, A \]
Now, calculate the total current \( I \):
\[ I = I_L + I_Z = 4.0 \, mA + 20.0 \, mA = 24.0 \, mA = 24.0 \times 10^{-3} \, A \]

### Step 4: Apply Ohm's Law to find the resistance \( R \)
Using Ohm's Law, we can find the resistance \( R \):
\[ R = \frac{V_R}{I} \]
Substituting the values we found:
\[ R = \frac{4.0 \, V}{24.0 \times 10^{-3} \, A} = \frac{4.0}{0.024} \approx 166.67 \, \Omega \]

### Step 5: Round the value of \( R \)
Since resistors come in standard values, we can round \( R \) to the nearest standard resistor value. Therefore, we can take:
\[ R \approx 167 \, \Omega \]

### Final Answer
The required value of the series resistor \( R \) is approximately \( 167 \, \Omega \).

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