Question

A change of $8mA$ in the emitter current brings a change of $7.9mA$ in collector current. How much change in base current is required to have the same change of $7.9mA$ in collector current? Find values of $\alpha$ and $\beta$.

Answer 1

Step1: Given data.

Change in emitter current $∆I_e=8mA$

Change in collector current $∆I_c=7.9mA$

Step2: Finding change in base current.

We know that,

For amplifier circuit change in emitter current is equal to sum of the change in collector and change in base current.

Mathematically express as:

$∆I_e=∆I_c+∆I_b$ $\left[\because ∆I_b=changeinbasecurrent\right]$

$\Rightarrow$$∆I_b=∆I_e-∆I_c$

$\Rightarrow$$∆I_b=8-7.9$

$\Rightarrow$$∆I_b=0.1mA$

Step3: Finding current gain $\mathit{\alpha }$ and $\mathit{\beta }$.

Also we know that,

For common-base-amplifier circuit current gain.

$\alpha =\frac{∆I_c}{∆I_e}=\frac{7.9mA}{8mA}=0.99$

For common-emitter-amplifier circuit current gain.

$\beta =\frac{∆I_c}{∆I_b}=\frac{7.9mA}{0.1mA}=79$

Hence, $\mathit{\alpha }\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{99}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathit{\beta }\mathbf{}\mathbf{=}\mathbf{}\mathbf{79}$