Question

For a common emitter amplifier, the audio signal voltage across the collector resistance of \(2\ \text{k}\Omega\) is 4 V. If the current amplification factor of the transistor is 100 and the base resistance is \(1\ \text{k}\Omega\), then the input voltage is

• A. \(10\ \text{mV}\)
• B. \(15\ \text{mV}\)
• C. \(20\ \text{mV}\)
• D. \(25\ \text{mV}\)

Hint:

Find the collector current from the output voltage, then the base current from the current gain, and multiply by the base resistance.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In a common emitter amplifier the current gain is \(\beta=\dfrac{I_C}{I_B}\). The input voltage is the voltage across the base resistance, \(V_i=I_BR_B\).

Step 2: Collector current
\(I_C=\dfrac{V_{out}}{R_C}=\dfrac{4}{2000}=2\times10^{-3}\) A.

Step 3: Base current
\(I_B=\dfrac{I_C}{\beta}=\dfrac{2\times10^{-3}}{100}=2\times10^{-5}\) A.

Step 4: Input voltage
\(V_i=I_BR_B=2\times10^{-5}\times1000=2\times10^{-2}\) V \(=20\) mV.

Final Answer:
The input voltage is 20 mV. \[ \boxed{\text{(C) }20\ \text{mV}} \]