A) \[{{g}_{m}}=\mu \times {{r}_{p}}\]
B) \[{{r}_{p}}=\mu \times {{g}_{m}}\]
C) \[\mu ={{r}_{p}}\times {{g}_{m}}\]
D) \[\mu =\frac{{{r}_{p}}}{{{g}_{m}}}\]
Correct Answer: C
Solution :
\[\mu ,\,\,{{r}_{p}}\] and \[{{g}_{m}}\] are three -constants of a triode valve, namely amplification factor, internal resistance and mutual conductance respectively. \[\mu =\left( \frac{\Delta {{V}_{p}}}{\Delta {{V}_{g}}} \right)\](for same amount of increase in\[{{i}_{p}}\]) \[{{r}_{p}}=\left( \frac{\Delta {{V}_{p}}}{\Delta {{V}_{p}}} \right)\] (while \[{{V}_{g}}\] is constant) and \[{{g}_{m}}\left( \frac{\Delta {{i}_{p}}}{\Delta {{V}_{g}}} \right)\] (while \[{{V}_{p}}\] is constant) We have, \[\mu =\frac{\Delta V}{\Delta {{V}_{g}}}=\frac{\Delta V}{\Delta {{i}_{p}}}\times \frac{\Delta {{i}_{p}}}{\Delta {{V}_{g}}}={{r}_{p}}\times {{g}_{m}}\] \[\therefore \] \[\mu ={{r}_{p}}\times {{g}_{m}}\]
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