For a transistor, α dc and β dc are the current ratios, then the value of α dc × β dc β dc − α dc

Question

For a transistor, α dc ​ and β dc ​ are the current ratios, then the value of α dc ​ × β dc ​ β dc ​ − α dc ​ ​

TestHub · Accepted Answer

The current ratios for a transistor are given by $α_{dc} = \frac{I _{C}}{I _{E}}$ and $β_{dc} = \frac{I _{C}}{I _{B}}$ .

The emitter current is the sum of base and collector currents:

$I_{E} = I_{B} + I_{C}$

Dividing the entire equation by $I_{C}$ , we get:

$\frac{I _{E}}{I _{C}} = \frac{I _{B}}{I _{C}} + 1$

Substituting the definitions of $α_{dc}$ and $β_{dc}$ :

$\frac{1}{α _{dc}} = \frac{1}{β _{dc}} + 1$

Rearranging the terms:

$\frac{1}{α _{dc}} - \frac{1}{β _{dc}} = 1$

$\frac{β _{dc} - α _{dc}}{α _{dc} \times β _{dc}} = 1$

Answer: 1

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