Question:
If A, B and C represent the power gain, base resistance and collector resistance respectively of a transistor connected in common emitter configuration, then the common emitter current amplification factor is:
If A, B and C represent the power gain, base resistance and collector resistance respectively of a transistor connected in common emitter configuration, then the common emitter current amplification factor is:
Show Hint
Remember the relation:
\[
\text{Power Gain}=(\text{Current Gain})^2\times\text{Resistance Gain}
\]
for a common emitter amplifier. This allows quick derivation of the required formula.
Updated On: Jun 15, 2026
- $\frac{\text{AB}}{\text{C}}$
- $\frac{\text{AC}}{\text{B}}$
- $\sqrt{\frac{\text{AC}}{\text{B}}}$
- $\sqrt{\frac{\text{AB}}{\text{C}}}$
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The Correct Option is D
Solution and Explanation
Concept:
For a transistor in common emitter configuration,
\[
\text{Power Gain}=\text{Current Gain}\times\text{Voltage Gain}
\]
If the current gain is $\beta$, then
\[
A_v=\beta\left(\frac{R_c}{R_b}\right)
\]
Therefore,
\[
A_p=\beta\times A_v
\]
\[
A_p=\beta^2\left(\frac{R_c}{R_b}\right)
\]
Step 1: Substitute the quantities given in the question Given, \[ A_p=A,\qquad R_b=B,\qquad R_c=C \] Hence, \[ A=\beta^2\left(\frac{C}{B}\right) \]
Step 2: Solve for $\beta$ \[ \beta^2=\frac{AB}{C} \] Taking square root, \[ \beta=\sqrt{\frac{AB}{C}} \] Therefore, \[ \boxed{\beta=\sqrt{\frac{AB}{C}}} \]
Step 1: Substitute the quantities given in the question Given, \[ A_p=A,\qquad R_b=B,\qquad R_c=C \] Hence, \[ A=\beta^2\left(\frac{C}{B}\right) \]
Step 2: Solve for $\beta$ \[ \beta^2=\frac{AB}{C} \] Taking square root, \[ \beta=\sqrt{\frac{AB}{C}} \] Therefore, \[ \boxed{\beta=\sqrt{\frac{AB}{C}}} \]
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