This question asks us to calculate the voltage gain ($A_v$) of a single-stage transistor amplifier given specific parameters: the collector load resistance ($R_C$), the input resistance ($R_i$), and the current gain ($A_i$).

Understanding Amplifier Parameters

• Collector Load ($R_C$): This is the resistance connected in the collector circuit of the transistor, which determines the output voltage swing. Given as $R_C = 2 \text{ k}\Omega$.
• Input Resistance ($R_i$): This is the effective resistance seen at the input terminals of the amplifier stage. Given as $R_i = 1 \text{ k}\Omega$.
• Current Gain ($A_i$): This is the ratio of the output current to the input current. Given as $A_i = 50$.
• Voltage Gain ($A_v$): This is the ratio of the output voltage to the input voltage. This is what we need to calculate.

Calculating Voltage Gain

The voltage gain ($A_v$) of a common-emitter transistor amplifier (or a similar single-stage amplifier) can be calculated using the following formula:

Where:

• $A_v$ is the voltage gain.
• $A_i$ is the current gain.
• $R_L$ is the load resistance. In this case, the collector load $R_C$ acts as the load resistance, so $R_L = R_C$.
• $R_i$ is the input resistance.

Applying the Formula

Let's substitute the given values into the formula:

• $A_i = 50$
• $R_L = R_C = 2 \text{ k}\Omega$
• $R_i = 1 \text{ k}\Omega$

Now, we calculate the voltage gain:

Result

The calculated voltage gain of the single-stage transistor amplifier is 100. This corresponds to the first option.