Question

In an n-p-n transistor amplifier, the collector current is 8 mA . If \(80 \%\) of the electrons from the emitter reach the collector, then ( \(\alpha\) and \(\beta\) are current ratios)

• A. the base current is 20 mA .
• B. the emitter current is 2 mA .
• C. \(\alpha =0.8,\beta =4.0\)
• D. \(\alpha =4.0,\beta =0.8\)

Hint:

Fraction of emitter electrons reaching the collector gives the current ratio alpha; use the emitter, base and collector current relation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
\(\alpha=\dfrac{I_C}{I_E}\) is the fraction of emitter current reaching the collector, and \(\beta=\dfrac{I_C}{I_B}\). Also \(I_E=I_B+I_C\).

Step 2: Find alpha
80 percent of the electrons reach the collector, so \(\alpha=0.8\).

Step 3: Find the currents
\(I_E=\dfrac{I_C}{\alpha}=\dfrac{8}{0.8}=10\text{ mA}\), and \(I_B=I_E-I_C=2\text{ mA}\).

Step 4: Find beta
\(\beta=\dfrac{I_C}{I_B}=\dfrac{8}{2}=4.0\), so \(\alpha=0.8,\ \beta=4.0\).

Final Answer:
The current ratios are \(\alpha=0.8\) and \(\beta=4.0\). \[ \boxed{\text{(C) }\alpha =0.8,\beta =4.0} \]