ElectricalElectronicseasyFE ExamCoursework

Collector Current from Base Drive

A BJT in the active region has a current gain $\beta = 100$ and a base current of $I_B = 50\ \mu\text{A}$ .

Find the collector current.

Given

β	100 -	Current gain
IB	50 uA	Base current

Hint 1

In the active region the collector current is a multiple of the base current.

Hint 2

I_C = βI_B.

Hint 3

Watch the prefix: 100 × 50 μA = 5000 μA.

Worked solution — try the problem first

In the active region:

$I_C = \beta I_B = 100 \times 50\ \mu\text{A} = 5000\ \mu\text{A} = 5.0\ \text{mA}$

$\boxed{I_C = 5.0\ \text{mA}}$

Emitter current follows from KCL at the device:

$I_E = I_B + I_C = 0.05 + 5.0 = 5.05\ \text{mA}$

Equivalently $I_E = (\beta+1)I_B$ .

The active-region caveat. This relation only holds while the transistor is not saturated. If the collector resistor is large enough that $\beta I_B$ would drive $V_{CE}$ below roughly 0.2 V, the device saturates and $I_C$ is set by the external circuit instead — always worth checking in a real design.

Concepts:BJT operationCurrent gainActive region

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