Q171 / 200 · Manipal (MET) 2013 · Physics

The correct relation between $\alpha$ and $\beta$ in a transistor is

  • Correct answer
    A
    $\beta=\frac{\alpha}{1-\alpha}$
  • B
    $\beta=\frac{\alpha}{1+\alpha}$
  • C
    $\beta=\frac{1+\alpha}{\alpha}$
  • D
    $\beta=1-\alpha$

Solution

We know that $\alpha=\left(\frac{\Delta i_C}{\Delta i_E}\right)$ .....(i) and $\quad \beta=\left(\frac{\Delta i_C}{\Delta i_B}\right)=\frac{\Delta i_C}{\Delta i_E} \times \frac{\Delta i_E}{\Delta i_B}$ $=\alpha \frac{\Delta i_E}{\Delta i_B}$ ....(ii) But $\Delta i_B=\Delta i_E-\Delta i_C$ from (ii) $\begin{aligned} & \beta=\alpha \frac{\Delta i_E}{\Delta i_E-\Delta i_C}=\frac{\alpha}{1-\frac{\Delta i_C}{\Delta i_E}} \\ & \therefore \beta =\frac{\alpha}{1-\alpha}\end{aligned}$

Hence, the correct answer is option: 'A'.

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