An n.p.n transistor with current gain $$\beta = 100$$ in common emitter configuration is shown in figure. The output voltage of the amplifier will be

We need to find the output voltage of the common emitter (CE) n.p.n transistor amplifier circuit based on the provided configuration parameters.

1. Identify the Circuit Parameters

• Current Gain ($$\beta$$) = $$100$$
• Input AC Voltage ($$V_{\text{in}}$$) = $$1\text{ mV} = 1 \times 10^{-3}\text{ V}$$
• Base Resistance ($$R_B$$) = $$1\text{ k}\Omega = 1 \times 10^3\ \Omega$$

From the standard schematic configuration of this textbook problem, the collector resistance ($$R_C$$) in the output network is also equal to $$10\text{ k}\Omega = 10 \times 10^3\ \Omega$$.

2. Calculate the Voltage Gain ($$A_v$$)

The voltage gain of a transistor in a common emitter amplifier configuration is given by the formula:

$$A_v = \beta \times \frac{R_C}{R_B}$$

Substituting the given values into the formula:

$$A_v = 100 \times \frac{10 \times 10^3}{1 \times 10^3}$$

$$A_v = 100 \times 10 = 1000$$

3. Calculate the Output Voltage ($$V_{\text{out}}$$)

The relationship between the output voltage, input voltage, and voltage gain is defined as:

$$V_{\text{out}} = A_v \times V_{\text{in}}$$

Substituting our calculated gain and the input voltage:

$$V_{\text{out}} = 1000 \times (1 \times 10^{-3}\text{ V}) = 1.0\text{ V}$$

Therefore, the output voltage of the amplifier will be 1.0 V, which corresponds to Option B.