A) \[500\]
B) \[1000\]
C) \[1250\]
D) \[100\]
Correct Answer: C
Solution :
Key Idea \[AC\] power gain is ratio of change in output power to the change in input power. \[AC\] power gain \[=\frac{Change\,\,in\,\,output\,\,power}{Change\,\,in\,\,input\,\,power}\] \[=\frac{\Delta {{V}_{c}}\times \Delta {{i}_{c}}}{\Delta {{V}_{i}}\times \Delta {{i}_{b}}}\] \[=\left( \frac{\Delta {{V}_{c}}}{\Delta {{V}_{i}}} \right)\times \left( \frac{\Delta {{i}_{c}}}{\Delta {{i}_{b}}} \right)=AV\times {{\beta }_{AC}}\] where \[{{A}_{V}}\] is voltage gain and \[{{(\beta )}_{AC}}\]is\[AC\] current gain. Also, \[{{A}_{V}}={{\beta }_{AC}}\times \text{resistance}\,\,\text{gain}\left( =\frac{{{R}_{o}}}{{{R}_{i}}} \right)\] Given,\[{{A}_{V}}=50\], \[{{R}_{o}}=200\,\,\Omega ,\,\,{{R}_{i}}=100\,\,\Omega \] 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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