Analysis of Bipolar Junction Transistor (BJT)

A Bipolar Junction Transistor (BJT) is a type of transistor that uses both electron and hole charge carriers. BJTs can be used as amplifiers, switches, or in other applications. Understanding the behavior and characteristics of BJTs is crucial for designing and analyzing circuits that incorporate them.

Correct Option Analysis

Option 1: I_E = [ I_C/β ] + βI_B

This option provides an expression involving the emitter current (I_E), collector current (I_C), and base current (I_B), along with the current gain (β) of the BJT.

To derive this expression, let's start with the basic relationships of currents in a BJT:

• The emitter current (IE) is the sum of the base current (IB) and the collector current (IC):
  I_E = I_B + I_C

The current gain (β) of a BJT is defined as the ratio of the collector current (IC) to the base current (IB):
β = I_C / I_B

From this, we can express the base current (IB) in terms of the collector current (IC) and β:
I_B = I_C / β

Substituting this expression for IB into the original equation for IE, we get:
I_E = (I_C / β) + I_C

Thus, the given expression I_E = [ I_C/β ] + βI_B is correct and aligns with the fundamental relationships of currents in a BJT.

Explanation of Other Options

Option 2: Collector current is the sum of emitter current and base current.

This statement is incorrect. The correct relationship is:
I_E = I_B + I_C
Here, the emitter current (I_E) is the sum of the base current (I_B) and the collector current (I_C), not the other way around.

Option 3: If β is the common emitter amplifier current gain, then I_C = βI_E

This statement is incorrect. The current gain β in a common emitter configuration is defined as:
β = I_C / I_B
Therefore, I_C = βI_B, not I_C = βI_E.

Option 4: The current gain in a common-base amplifier is the ratio of collector current to base current.

This statement is incorrect. The current gain in a common base amplifier configuration is denoted by α and is defined as:
α = I_C / I_E
α is typically close to unity and differs from the current gain β in a common emitter configuration.