In a common‑emitter configuration, which statement correctly describes the relationship between collector curr

Question

In a common‑emitter configuration, which statement correctly describes the relationship between collector current (Ic) and base current (Ib) for a silicon NPN transistor operating in the active region?

Examoogle · Accepted Answer

The correct answer is Option A: Ic ≈ β × Ib. In the active region, a bipolar junction transistor (BJT) acts as an amplifier where the collector current ($I_c$) is directly proportional to the base current ($I_b$) through the common-emitter current gain ($\beta$).

Step-by-Step Solution & Concepts:
In the active region, a bipolar junction transistor (BJT) acts as an amplifier where the collector current ($I_c$) is directly proportional to the base current ($I_b$) through the common-emitter current gain ($\beta$).

Working Principle: In a silicon NPN transistor operating in the active region, the emitter-base junction is forward-biased and the collector-base junction is reverse-biased. Electrons injected from the emitter into the base mostly diffuse across to the collector due to the strong reverse-bias electric field, establishing the collector current as a multiple ($\beta$) of the base current.

Key Formulas: $I_c \approx \beta 	imes I_b$ — Collector current in common-emitter mode; $\beta = \frac{\alpha}{1 - \alpha}$ — Relationship between common-emitter and common-base current gains

Key Points: The emitter-base junction is forward-biased and the collector-base junction is reverse-biased in the active region.; The common-emitter current gain $\beta$ typically ranges between 50 and 300 for standard silicon BJTs.; Collector current is primarily controlled by the input base current in the common-emitter configuration.

Advantages: High current gain and power gain; Widely used in voltage and power amplification stages

Disadvantages: Sensitive to temperature variations affecting $\beta$ and leakage current; Lower bandwidth compared to common-base configurations

Applications: Audio and radio-frequency amplifiers; Linear voltage regulators and electronic switches

Additional Info: Option A is correct because $I_c \approx \beta 	imes I_b$ defines the active region relationship in a common-emitter configuration.. Option C ($I_c \approx \alpha 	imes I_E$) corresponds to the common-base configuration.

Answer: A is correct — The collector current in a common-emitter configuration operating in the active region is approximately equal to the product of the base current and the common-emitter current gain ($I_c \approx \beta 	imes I_b$).

Exam Tip: Remember the conversion formula $\beta = \frac{\alpha}{1 - \alpha}$ as exam questions frequently require interconverting common-base and common-emitter parameters.

Examoogle · Answer

Option B: Ic = VCE / RE

Examoogle · Answer

Option C: Ic ≈ α × IE

Examoogle · Answer

Option D: Ic = β × (VBE – 0.7 V)

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