# Given $\Delta V_{BE} =$ potential difference across base emitter, $\Delta I_C =$ change in collector current, $\Delta I_B =$ change in the base current and $\Delta R_{BE} =$ change in base emitter resistance, which of the following best represents transconductance $g_m$.

$(a)\;\frac{\Delta V_{BE}}{\Delta I_c} \\ (b)\;\frac{\Delta R_{BE}}{\Delta I_c} \\ (c)\;\frac{\Delta I_c}{\Delta I_B} \\ (d)\;\frac{\Delta I_c}{\Delta v_{BE}}$

where

$\Delta V_{BE}$ -Potential difference across base emitter

$\Delta I_C$- charge in collector current

$\Delta I_B$- change in base current

$\Delta R_{BE}$ change in base- emitter resistance

The property to measure amplification in a transistor used an amplifier circuit is called transconductance.
To have large amplification a small change in $V_{BE}$ due to input signal, should result in large change in collector current $I_C$
Transconductane $g_m =\large\frac{\Delta I_c}{\Delta V_{BE}}$
Hence d is the correct answer.
edited Jul 14, 2014