• # question_answer Output characteristics of an n-p-n transistor in CE configuration is shown in the below figure. Determine : (i) DC current gain. (ii) Dynamic output resistance. (iii) AC current gain at an operating point, ${{V}_{CE}}=10V,\,\,when\,\,{{I}_{B}}=30\mu A.$

(i) According to the question, ${{I}_{B}}=30\mu A,$ ${{V}_{CE}}=10\,V$ and ${{I}_{C}}=3.5mA$ DC current gain             ${{\beta }_{DC}}=\frac{{{I}_{C}}}{{{I}_{B}}}=\frac{3.5\,mA}{0.030\,mA}=117$ (ii) Dynamic output resistance is given by             ${{r}_{0}}=\left( \frac{\Delta \,{{V}_{CE}}}{\Delta {{I}_{c}}} \right)$ For ${{I}_{B}}=30\mu A,$ $\Delta {{V}_{CE}}=12-8=4\,V,$ $\Delta {{I}_{C}}=3.6-3.4=0.2\,mA.$ $\therefore$      ${{r}_{0}}=\frac{4\,V}{0.2\,mA}=\frac{4}{0.2\times {{10}^{-3}}}=2\times {{10}^{4}}\Omega$ (iii) AC current gain, ${{\beta }_{AC}}={{\left( \frac{\Delta {{I}_{C}}}{\Delta {{I}_{B}}} \right)}_{{{V}_{CE}}}}$ At ${{V}_{CE}}=10\,V,$ $\Delta {{I}_{C}}=(3.5-2.5)\,mA=1mA$ and $\Delta {{I}_{B}}=30\mu A-20\mu A=10\mu A$ $\therefore$ ${{\beta }_{AC}}=\frac{1\,mA}{10\,\mu A}=100$