Question

\(\beta\), \(R_{L}\) and \(r\) are the a.c. current gain, load resistance and the input resistance of a transistor respectively in common emitter configuration, the voltage gain and the power gain are respectively

• A. \(\beta (R_{L}/r)\) and \(\beta ^{2}(R_{L}/r)\)
• B. \(\beta (r/R_{L})\) and \(\beta ^{2}(r/R_{L})\)
• C. \(\beta (R_{L}/r)\) and \(\beta (R_{L}/r)^{2}\)
• D. \(\beta (r/R_{L})\) and \(\beta (r/R_{L})^{2}\)

Hint:

Voltage gain is the current gain times the ratio of load to input resistance, and power gain is current gain times voltage gain.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
In common emitter mode the a.c. current gain is \(\beta\), the output (load) resistance is \(R_L\) and the input resistance is \(r\).

Step 2: Voltage gain
\(A_V=\dfrac{V_{out}}{V_{in}}=\dfrac{\beta I_BR_L}{I_Br}=\beta\dfrac{R_L}{r}\).

Step 3: Power gain
\(A_P=\beta\times A_V=\beta\cdot\beta\dfrac{R_L}{r}=\beta^2\dfrac{R_L}{r}\).

Step 4: Compare the options
This matches option (A).

Final Answer:
The voltage gain is beta R_L over r and the power gain is beta squared R_L over r. \[ \boxed{\text{(A) }\beta\left(\dfrac{R_L}{r}\right)\text{ and }\beta^{2}\left(\dfrac{R_L}{r}\right)} \]