What is power gain?

Hint: It is related to transistors. The term Power gain is most commonly used when the transistor is used as an amplifier.In a single line power gain can be expressed as the ratio of output power to the Input Power.

Complete answer:
 It can also be said the power gain is the product of voltage gain and current gain. Power gain is a ratio between two quantities and hence is dimensionless. In CE transistors, the current gain is defined as the ratio of change in collector current and change in base current.
Hence current gain
$\beta = \dfrac{{\Delta {I_c}}}{{\Delta {I_b}}}
\Rightarrow\beta= \dfrac{{{i_c}}}{{{i_b}}}$
Where ${i_c}$ is the change in collector current and ${i_b}$ is the change in base current of the transistor

The voltage gain is defined as the ratio of output voltage and input voltage.
Hence the voltage gain of the amplifier ${A_v} = \dfrac{{{v_o}}}{{{v_i}}}$
Where ${v_o}$ is the output voltage and ${v_i}$ is the input voltage to the transistor.

Now the output voltage can be defined as the change in ${V_{CE}}$ .Thus we can say that $\Delta {V_{CE}} = \beta {R_L}\Delta {I_B}$
${A_v} = \dfrac{{{v_o}}}{{{v_i}}}\\
\Rightarrow{A_v}= \dfrac{{\Delta {V_{CE}}}}{{r\Delta {I_B}}} \\
\therefore{A_v}= \dfrac{{\beta {R_L}}}{r}$
Here $r$ is the sum of input resistance and resistance across the base terminal and ${R_L}$ is the load resistance.

The power gain can finally be expressed as ${A_p} = \beta \times {A_v} = \dfrac{{{\beta ^2}{R_L}}}{r}$.

Note: The transistors can also be used in different ways. They can also be used as an oscillator or switch. Transistors are a part of pure electronics. Students generally find it difficult to remember the terms as there are many formulas. Hence these should be studied thoroughly.