In a silicon transistor, a change of 7.89 mA in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce an equivalent change in the collector current?

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Solution

Given,
Change in emitter current, ΔI_e = 7.89 mA
Change in collector current, ΔI_c = 7.8 mA

Since,
Current gain,

α_{ac} = \frac{∆ I_{c}}{∆ I_{e}} = \frac{7.8}{7.89} = 0.9886

and,

Voltage gain,

β_{ac} = \frac{α}{1 - α} = \frac{0.9886}{1 - 0.9886} = 86.72

Also since,

β_{ac} = \frac{∆ I_{c}}{∆ I_{b}}

\Rightarrow

Change in base current, ∆ I_{b} = \frac{∆ I_{c}}{β_{ac}} = \frac{7.8}{86.72} = 89.94 \times 10^{- 3} mA .

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