A) 500
B) 1000
C) 1250
D) 100
Correct Answer: C
Solution :
\[AC\,\,power\,\,gain=\frac{Change\,\,in\,\,output\,\,power}{Change\,\,in\,\,input\,\,power}\] \[=\,\,\,\frac{\Delta {{V}_{c}}\times \Delta {{i}_{c}}}{\Delta {{V}_{i}}\times \Delta {{i}_{b}}}=\left( \frac{\Delta {{V}_{c}}}{\Delta {{V}_{i}}} \right)\times \left( \frac{\Delta {{i}_{c}}}{\Delta {{i}_{b}}} \right)\] where Ay is voltage gain and \[{{\left( \beta \right)}_{AC}}\] current gain. Also, \[{{A}_{V}}={{\beta }_{AC}}\times resis\tan ce\,\,gain\,=\left( \frac{{{R}_{0}}}{{{R}_{i}}} \right)\] Given, \[\operatorname{A}{{ & }_{V}}=\,\,50,\,\,{{R}_{o}}=\,\,200\,\,\Omega ,\,\,\,{{R}_{i}}\,\,=\,\,100\,\Omega \] Hence, \[50={{\beta }_{AC}}\times \frac{200}{100}\] \[\therefore \,\,\,\,\,\,\,{{\beta }_{AC}}\,\,=\,\,25\] Now, AC power gain \[\,=\,\,\,\,{{A}_{V}}\times {{\beta }_{AC}}\] \[=\,\,\,50\times 25=1250\]
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