A p-n junction in series with a resistance of `5 kOmega` is connected across a 50 V DC source . If the forward bias resistance of the junction is `50 Omega` , the forward bias current is

Options

A. (a)1 mA
B. 2 mA
C. 20 mA
D. 9.9 mA

Answer

To solve the problem of finding the forward bias current in a p-n junction connected in series with a resistance, we can follow these steps:

### Step 1: Understand the Circuit Configuration
We have a p-n junction diode in forward bias connected in series with a resistor of \(5 \, k\Omega\) (which is \(5000 \, \Omega\)) and a \(50 \, V\) DC source. The forward bias resistance of the junction is given as \(50 \, \Omega\).

### Step 2: Convert Units
To simplify calculations, we can convert the forward bias resistance from ohms to kilo-ohms:
\[ 50 \, \Omega = \frac{50}{1000} \, k\Omega = 0.05 \, k\Omega \]

### Step 3: Calculate Total Resistance
Since the resistor and the forward bias resistance of the diode are in series, we can find the total resistance \(R_{total}\) by adding both resistances:
\[ R_{total} = R_{series} + R_{diode} = 5000 \, \Omega + 50 \, \Omega = 5050 \, \Omega \]

### Step 4: Apply Ohm's Law
Using Ohm's Law, we can find the forward bias current \(I\) flowing through the circuit. The formula for current is:
\[ I = \frac{V}{R_{total}} \]
Substituting the values:
\[ I = \frac{50 \, V}{5050 \, \Omega} \]

### Step 5: Calculate the Current
Now we perform the calculation:
\[ I = \frac{50}{5050} \approx 0.0099 \, A \]
To convert this into milliamperes (mA):
\[ I \approx 0.0099 \, A \times 1000 \approx 9.9 \, mA \]

### Step 6: Conclusion
The forward bias current is approximately \(9.9 \, mA\).

### Final Answer
The forward bias current is \(9.9 \, mA\).

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