A) \[\frac{25}{24}\]
B) \[\frac{24}{25}\]
C) \[\frac{25}{26}\]
D) \[\frac{26}{25}\]
Correct Answer: B
Solution :
Key Idea: Emitter current is sum of base current and collector current. The current gain \[(\alpha )\] for a transistor is given by \[\alpha =\frac{\Delta {{\Iota }_{C}}}{\Delta {{I}_{E}}}\] ?(i) Also, \[\Delta {{\Iota }_{E}}=\Delta {{\Iota }_{C}}+\Delta {{\Iota }_{B}}\] ?(ii) From Eqs. (i) and (ii), we get \[\alpha =\frac{\Delta {{\Iota }_{E}}-\Delta {{\Iota }_{B}}}{\Delta {{\Iota }_{E}}}\] Given, \[\Delta {{\Iota }_{E}}=25\,mA,\,\Delta {{\Iota }_{B}}=1\,mA\] \[\therefore \] \[\alpha =\frac{25-1}{25}=\frac{24}{25}\] Note: Current gain \[(\alpha )\] is usually less than one, hance, options [a] and [d] cannot be correct.
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