Question

In a common emitter transistor amplifier, the audio signal voltage across the collector resistance of \(2\,k\Omega\) is \(2V\). If the current amplification factor (\(\beta\)) is \(100\) and the base resistance is \(1\,k\Omega\), find the input signal voltage.

• A. \(0.1\,V\)
• B. \(0.01\,V\)
• C. \(0.02\,V\)
• D. \(0.005\,V\)

Hint:

For a common emitter amplifier: \[ A_v = \beta \left(\frac{R_C}{R_B}\right) \] Once the voltage gain is known, input voltage can be quickly found using \[ V_{in} = \frac{V_{out}}{A_v}. \]

Answer 1

The Correct Option is B

Concept: In a common emitter amplifier, the voltage gain is given by \[ A_v = \beta \left(\frac{R_C}{R_B}\right) \] where \(\beta\) = current amplification factor, \(R_C\) = collector resistance, \(R_B\) = base resistance. Also, \[ A_v = \frac{\text{Output Voltage}}{\text{Input Voltage}} \]

Step 1: Calculate the voltage gain. Given \[ \beta = 100,\quad R_C = 2k\Omega = 2000\Omega,\quad R_B = 1k\Omega = 1000\Omega \] \[ A_v = \beta \left(\frac{R_C}{R_B}\right) \] \[ A_v = 100 \times \frac{2000}{1000} \] \[ A_v = 100 \times 2 = 200 \]

Step 2: Use the relation between input and output voltage. \[ A_v = \frac{V_{out}}{V_{in}} \] Given output voltage \[ V_{out} = 2V \]

Step 3: Calculate the input signal voltage. \[ V_{in} = \frac{V_{out}}{A_v} \] \[ V_{in} = \frac{2}{200} \] \[ V_{in} = 0.01\,V \] \[ \boxed{V_{in} = 0.01\,V = 10\,mV} \]