DC current gain computation (BJT): A transistor has a current gain (β) of 175. If the base current is 0.1 mA, calculate the collector current.

Introduction / Context:For a bipolar junction transistor (BJT) operating in the active region, the DC current gain β (also written h_FE) relates collector current to base current as I_C = β * I_B. This quick calculation is routine when sizing bias networks, estimating load current capability, or checking feasibility.

Given Data / Assumptions:

• β = 175 (dimensionless DC current gain).
• I_B = 0.1 mA.
• Transistor assumed to be in forward-active operation (not saturated).

Concept / Approach:Use the definition of DC current gain: I_C = β * I_B. Ensure units are consistent. Convert milliampere if desired, but here the numbers multiply cleanly without conversion as long as we keep track of the decimal places.

Step-by-Step Solution:Write formula: I_C = β * I_B.Substitute: I_C = 175 * 0.1 mA.Compute: 175 * 0.1 = 17.5.Therefore, I_C = 17.5 mA.

Verification / Alternative check:Convert base current to amperes: 0.1 mA = 0.0001 A. Then I_C = 175 * 0.0001 A = 0.0175 A = 17.5 mA. Same result.

Why Other Options Are Wrong:(a) 1750 mA is 100 times too large (as if β = 1750 or I_B misread). (c) 175 mA is 10 times too large. (d) 1.75 mA is 10 times too small. (e) Invalid since a correct answer exists.

Common Pitfalls:Confusing β with gain in percent; misplacing the decimal with milliampere units; applying the formula when the device is saturated (where the β relation breaks down).

Final Answer:17.5 mA.