Bipolar transistor current gain (β) relation: If the current gain β = I_C / I_B is 200 and the collector current I_C is 100 mA, what is the base current I_B?

Introduction / Context:The small-signal or DC current gain of a BJT is defined as β = I_C / I_B. Rearranging gives I_B = I_C / β. This quick calculation appears frequently in biasing design and when estimating drive requirements from preceding stages or controllers.

Given Data / Assumptions:

• I_C = 100 mA.
• β = 200 (dimensionless).
• Steady-state DC bias; ignore leakage currents.

Concept / Approach:Use the definition of current gain to solve for the unknown base current. Ensure units are consistent and convert the final result to mA for clarity.

Step-by-Step Solution:Start with β = I_C / I_B.Rearrange: I_B = I_C / β.Substitute: I_B = 100 mA / 200 = 0.5 mA.State clearly: base current is 0.5 mA.

Verification / Alternative check:Back-check: β * I_B = 200 * 0.5 mA = 100 mA = I_C, confirming consistency.

Why Other Options Are Wrong:(a) 2 mA would imply β = 50. (c) and (d) are wildly off by orders of magnitude. “None” is unnecessary since an exact match exists.

Common Pitfalls:Unit mix-ups (mA vs A) and arithmetic slips when dividing by β.

Final Answer:0.5 mA