A) \[\mu ={{r}_{p}}\times {{g}_{m}}\]
B) \[{{r}_{p}}=\mu \times {{g}_{m}}\]
C) \[{{g}_{m}}=\mu \times {{r}_{p}}\]
D) none of these
Correct Answer: A
Solution :
The amplification factor \[\left( \mu \right)\] is given by \[\mu ={{\left( \frac{\Delta {{V}_{P}}}{\Delta {{V}_{g}}} \right)}_{{{I}_{P}}=\operatorname{constant}}}\] ? (i) Plate resistance \[{{r}_{P}}={{\left( \frac{\Delta {{V}_{P}}}{\Delta {{I}_{g}}} \right)}_{{{V}_{g}}=\text{constant}}}\] ? (ii) Transconductance \[{{g}_{m}}={{\left( \frac{\Delta {{I}_{P}}}{\Delta {{V}_{g}}} \right)}_{{{V}_{P}}=\text{constant}}}\] ? (iii) \[\therefore \] \[\mu =\frac{\Delta {{V}_{p}}}{\Delta {{V}_{g}}}=\frac{\Delta {{V}_{P}}}{\Delta {{I}_{P}}}\times \frac{\Delta {{I}_{p}}}{\Delta {{V}_{g}}}\] From Eqs. (ii) and (iii), we get \[\mu ={{r}_{p}}\times {{g}_{m}}\]
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