The potential difference across the collector of a transistor, used in common emitter mode is 1.5 V , with the collector resistance $3k\Omega$. Find the emitter current in mA , if gain of transistor is 50.

$$\begin{gathered} V_{CE}=1.5V, \\ {R}_C=3k\Omega =3000\Omega , \end{gathered}$$

$\beta =50$

$i_e=?$

$We know that, i_e=i_b+i_c .............\left(1\right)$

$Ohm\text{'}s Law across output side, i_c=\frac{V_{CE}}{R_C}=\frac{1.5}{3000}=0.5\times {10}^{-3}A$

$$\begin{gathered} Gain , \beta =\frac{I_c}{I_b} \\ \Rightarrow I_b=\frac{I_c}{\beta }=\frac{0.5\times {10}^{-3}}{50}=0.01\times {10}^{-3}A, \end{gathered}$$

$$\begin{gathered} I_e=I_b+I_c \\ =0.01\times {10}^{-3}+0.50\times {10}^{-3} \\ =0.51\times {10}^{-3}=0.51mA \end{gathered}$$