For a BJT, determine the emitter current if the collector current is 1 mA and the common base short circuit amplification factor is unity. 

Emitter Current in BJT (Bipolar Junction Transistor):

Definition: The emitter current (I_E) in a Bipolar Junction Transistor (BJT) is the total current flowing out of the emitter terminal. It is the sum of the base current (I_B) and the collector current (I_C).

Important Parameters:

• Collector Current (I_C): The current flowing through the collector terminal.
• Base Current (I_B): The current flowing through the base terminal.
• Emitter Current (I_E): The total current flowing out of the emitter terminal, given by:

Formula:

The emitter current can be expressed as:

I_E = I_C + I_B

Additionally, the common base short circuit current gain, denoted by α, relates the collector current to the emitter current:

α = I_C / I_E

Rearranging the formula, we can write:

I_E = I_C / α

Given Data:

• Collector Current, I_C = 1 mA
• Common Base Short Circuit Current Gain, α = 1 (unity)

Solution:

Using the formula:

I_E = I_C / α

Substitute the given values:

I_E = 1 mA / 1

I_E = 1 mA

Hence, the emitter current is 1 mA.

Correct Option Analysis:

The correct option is:

Option 3: 1 mA

This option is correct because the emitter current is calculated to be 1 mA based on the given collector current and the common base short circuit current gain (α = 1). The result directly matches the provided data and the relationship between these parameters in the BJT.

Additional Information

To further understand the analysis, let’s evaluate why the other options are incorrect:

Option 1: 1.5 mA

This option suggests that the emitter current is 1.5 mA. However, the given parameters (I_C = 1 mA and α = 1) clearly show that the emitter current is 1 mA. A value of 1.5 mA would imply a different value of α, which is not consistent with the problem statement.

Option 2: 2 mA

This option proposes an emitter current of 2 mA. This value is incorrect because, with α = 1, the emitter current must equal the collector current. An emitter current of 2 mA would require a collector current greater than 1 mA, which contradicts the given data.

Option 4: 0.5 mA

This option suggests an emitter current of 0.5 mA. This is incorrect because, with α = 1, the emitter current cannot be less than the collector current. A value of 0.5 mA for the emitter current would imply either an incorrect value of α or collector current, which is not the case here.

Conclusion:

Understanding the relationship between emitter current, collector current, and the common base current gain (α) is essential in analyzing BJTs. In this case, the emitter current is directly equal to the collector current due to the unity gain (α = 1). This simplicity highlights the importance of correctly applying the fundamental formulas of BJT operation.