Question

In common emitter connection, the collector leakage current in a transistor is 300\(\mu\)A. The leakage current in the transistor in common base arrangement will be (Given \(\beta\) = 130):

• A. 2.28 \(\mu\)A
• B. 2.28 mA
• C. 2.28 A
• D. 22.8 \(\mu\)A

Hint:

Remember that the leakage current in the common emitter configuration (\(I_{CEO}\)) is always significantly larger than in the common base configuration (\(I_{CBO}\)) by a factor of (\(\beta+1\)). This is because the small \(I_{CBO}\) is amplified by the transistor action in the CE setup.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In a Bipolar Junction Transistor (BJT), leakage current is the small current that flows even when the transistor is supposed to be "off". This current is temperature-dependent. The leakage current is defined differently for common emitter (CE) and common base (CB) configurations.
\( I_{CEO} \): Collector-to-Emitter leakage current with the base open (for CE configuration).
\( I_{CBO} \): Collector-to-Base leakage current with the emitter open (for CB configuration).
These two leakage currents are related through the transistor's current gain parameters.
Step 2: Key Formula or Approach:
The relationship between the common emitter leakage current (\( I_{CEO} \)) and the common base leakage current (\( I_{CBO} \)) is given by:
\[ I_{CEO} = (\beta + 1) I_{CBO} \] where \(\beta\) is the common emitter DC current gain. We are given \( I_{CEO} \) and \(\beta\) and need to find \( I_{CBO} \).
Step 3: Detailed Explanation:
1. Identify the given values:
Common emitter leakage current, \( I_{CEO} = 300 \, \mu A \).
Common emitter current gain, \( \beta = 130 \).
2. Rearrange the formula to solve for \( I_{CBO} \):
\[ I_{CBO} = \frac{I_{CEO}}{\beta + 1} \] 3. Substitute the values and calculate:
\[ I_{CBO} = \frac{300 \, \mu A}{130 + 1} \] \[ I_{CBO} = \frac{300}{131} \, \mu A \] \[ I_{CBO} \approx 2.290 \, \mu A \] Step 4: Final Answer:
The calculated value for the common base leakage current is approximately 2.29 \(\mu\)A. The closest option is 2.28 \(\mu\)A.