Relation Between Transistor Current Gains Alpha And Beta

Relation Between Transistor Current Gains Alpha And Beta — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.

Relation between Transistor Current Gains (Alpha and Beta) Applicable to Bipolar Junction Transistors (BJT) generally considered in the active region of operation where emitter current is split into base and collector currents. Start with the fundamental BJT current equation: I E = I C + I B . Divide the entire equation by collector current I C : I E I C = 1 + I B I C . Substitute the definitions of gains: 1 = I E I C and 1 = I B I C . Equation becomes 1 = 1 + 1 = + 1 . Invert both sides to get = 1 + . Applies only to BJTs, not FETs. Assumes leakage currents (ICBO) are negligible for the simplified ratio. Alpha is strictly less than 1. Confusing Alpha with Beta; Beta is usually large (20-500), Alpha is close to 1 (0.95-0.99). Assuming Alpha can be greater than 1 (it cannot, as collector current cannot exceed emitter current). Mixing up the conversion formula signs (e.g., using 1-beta instead of 1+beta).