Question

In a common emitter transistor amplifier circuit, the input resistance is 1.8 k$\Omega$ and output is obtained across a load resistance of 9 k$\Omega$. The alternating current gain is 70. Corresponding to an a.c. input voltage of 6 mV, the output voltage will be ______.

• A. 0.7 V
• B. 1.4 V
• C. 2.1 V
• D. 4.2 V

Hint:

Power Gain is the big brother here! $A_P = \beta \times A_v = \beta^2 \times (R_{\text{out}}/R_{\text{in}})$. Remember that Voltage Gain directly depends on both the current gain AND the ratio of the resistors!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given parameters for a common emitter (CE) transistor amplifier: input/output resistances, AC current gain, and input voltage. We need to calculate the amplified output voltage.

Step 2: Detailed Explanation:
The fundamental property of an amplifier is its Voltage Gain ($A_v$), which is the ratio of output voltage to input voltage.
$A_v = \frac{V_{\text{out}}}{V_{\text{in}}}$
The Voltage Gain can also be calculated using the transistor's internal parameters. Voltage gain is the product of Current Gain ($\beta$) and Resistance Gain (ratio of output resistance to input resistance).
$A_v = \beta \times \left( \frac{R_{\text{out}}}{R_{\text{in}}} \right)$
We are given the following values:
Current gain ($\beta$) = 70
Input resistance ($R_{\text{in}}$) = $1.8 \text{ k}\Omega = 1800 \ \Omega$
Output/Load resistance ($R_{\text{out}}$) = $9 \text{ k}\Omega = 9000 \ \Omega$
Input voltage ($V_{\text{in}}$) = $6 \text{ mV} = 6 \times 10^{-3} \text{ V}$
First, calculate the Voltage Gain ($A_v$):
$A_v = 70 \times \left( \frac{9000}{1800} \right)$
$A_v = 70 \times 5$
$A_v = 350$
This means the amplifier boosts any input voltage by a massive factor of 350.
Now, calculate the output voltage ($V_{\text{out}}$):
$V_{\text{out}} = A_v \times V_{\text{in}}$
$V_{\text{out}} = 350 \times (6 \times 10^{-3} \text{ V})$
Calculate the multiplication:
$350 \times 6 = 2100$
$V_{\text{out}} = 2100 \times 10^{-3} \text{ V}$
Adjust the decimal to standard units:
$V_{\text{out}} = 2.1 \text{ V}$

Step 3: Final Answer:
The output voltage is 2.1 V, matching option (c).