In a zener regulator, if source voltage is 30 V, series resistance is of `1.5kOmega,` load resistance is of `2kOmega` and `V_(z)`=10 V, the zener current will be

Options

A. 13.33mA
B. 5 mA
C. 10 mA
D. 8.33 mA

Answer

To find the Zener current in a Zener regulator circuit, we can follow these steps:

### Step 1: Identify the given values
- Source Voltage (V_s) = 30 V
- Series Resistance (R_s) = 1.5 kΩ = 1500 Ω
- Load Resistance (R_L) = 2 kΩ = 2000 Ω
- Zener Voltage (V_z) = 10 V

### Step 2: Calculate the load current (I_L)
The load current can be calculated using Ohm's law. The voltage across the load is equal to the Zener voltage (V_z).

\[ I_L = \frac{V_z}{R_L} = \frac{10 \, \text{V}}{2000 \, \Omega} = 0.005 \, \text{A} = 5 \, \text{mA} \]

### Step 3: Calculate the source current (I_s)
The source current can be calculated by first finding the voltage drop across the series resistance (R_s). The voltage drop across R_s can be calculated as:

\[ V_{R_s} = V_s - V_z = 30 \, \text{V} - 10 \, \text{V} = 20 \, \text{V} \]

Now, using Ohm's law, we can find the source current:

\[ I_s = \frac{V_{R_s}}{R_s} = \frac{20 \, \text{V}}{1500 \, \Omega} \approx 0.01333 \, \text{A} = 13.33 \, \text{mA} \]

### Step 4: Calculate the Zener current (I_z)
The Zener current can be found using the relationship between the source current, load current, and Zener current:

\[ I_s = I_z + I_L \]

Rearranging this gives:

\[ I_z = I_s - I_L \]

Substituting the values we calculated:

\[ I_z = 13.33 \, \text{mA} - 5 \, \text{mA} = 8.33 \, \text{mA} \]

### Final Answer
The Zener current (I_z) is approximately **8.33 mA**.

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