# In a transistor if I_c/I_e=alpha and I_c/I_b=beta, if alpha varies between (20)/(21) and (100)/(101), then the value of beta lied between?

Mar 1, 2017

$20 \mathmr{and} 100$

#### Explanation:

Representative circuit in Common emitter amplifier configuration is given below

Given is the ratio of ${I}_{c} / {I}_{b} = \beta$
And the ratio of ${I}_{c} / {I}_{e} = \alpha$

From above expressions we have
${I}_{c} = \beta {I}_{b} = \alpha {I}_{e}$ .....(1)

In this configuration, the current flowing out of the transistor must be equal to the currents flowing into the transistor. As such we have

${I}_{e} = {I}_{c} + {I}_{b}$ .....(2)

To have a combined the expression for α and β we divide both sides of (2) by ${I}_{b}$ and use (1) to get

${I}_{e} / {I}_{b} = \frac{{I}_{c} + {I}_{b}}{I} _ b$
$\implies \frac{\beta}{\alpha} = \beta + 1$
$\implies \beta = \alpha \beta + \alpha$

$\implies \beta = \frac{\alpha}{1 - \alpha}$

For $\alpha = \frac{20}{21}$

$\beta = \frac{\frac{20}{21}}{1 - \frac{20}{21}} = 20$

Again for $\alpha = \frac{100}{101}$
$\beta = \frac{\frac{100}{101}}{1 - \frac{100}{101}} = 100$
.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-

Note: value of $\alpha$ will always be$< 1$.
and typically, $\beta$ values lie between $20 \mathmr{and} 200$ for most general purpose transistors.