Question

What is the voltage gain in a common emitter amplifier, when input resistance is 3Ω and load resistance is 24Ω with β = 60?
A. 480
B. 2.4
C. 4.8
D. 8.4

Answer 1

Hint: To calculate the required voltage gain we take the formula:- $$\text{Voltage gain = }\beta \left({\displaystyle \frac{R_{output}}{R_{input}}}\right)$$, where, $$\beta \text{ is voltage amplification factor}$$
$$R_{output}$$, $$R_{input}$$ are the output( load) input and output resistances respectively.

Complete step-by-step answer:
To find the required voltage gain.
The formula used: $$\text{Voltage gain = }\beta \left({\displaystyle \frac{R_{output}}{R_{input}}}\right)$$ …………….(i)
Given:-
$$\begin{gathered} \beta =60 \\ {R}_{output}=24\mathrm{\Omega }\text{ and }{R}_{input}=3\mathrm{\Omega } \end{gathered}$$
Substituting the given values of $$\beta ,R_{output}\text{ and }{R}_{input}=3\mathrm{\Omega }\text{ in eqn(i)}$$we get
$$\begin{gathered} \text{Voltage gain = 60}\times \left({\displaystyle \frac{24}{3}}\right)V \\ \Rightarrow \text{Voltage gain = }60\times 8\text{ V} \\ \Rightarrow \text{Voltage gain = 480 V} \end{gathered}$$
Hence Option (A) is the correct answer.

Note: To solve such kinds of questions one should have to revise the short formulae in this of this topic with the basic algorithm behind deducing the expressions involving terms like voltage gain, amplification factors input, and the load or output resistance. Always start with what is given in questions and what we will have to find.