Why BJTs Need Forced Beta for Saturation
A Bipolar Junction Transistor (BJT) can operate in three regions: Cutoff (fully off), Active/Linear (amplification), and Saturation (fully turned on as a switch). In data sheets, the DC current gain (h_{FE}) is specified exclusively for the linear amplification region.
If you calculate base current simply as (I_b = I_c / h_{FE}), the transistor will hover on the edge of the active region. The collector-emitter voltage (V_{ce}) will float at 1V to 3V, causing massive heat dissipation ((P = V_{ce} imes I_c)) that burns out the transistor!
The Universal Forced Beta Rule ((eta_{ ext{forced}} = 10))
To guarantee that (V_{ce}) collapses to its minimum saturation voltage ((V_{ ext{ce(sat)}} approx 0.1 ext{V} - 0.2 ext{V})), semiconductor manufacturers recommend a forced beta of 10:1 (i.e. supplying (I_b = I_c / 10)).
Protecting Microcontroller GPIO Pins
Microcontrollers have strict maximum current limits per GPIO pin (e.g. 20 mA for Arduino ATmega328P, 12 mA for ESP32, and 8 mA for Raspberry Pi). If your load requires (I_c = 500 ext{ mA}), forced beta ((50 ext{ mA})) will destroy the MCU pin! In such cases, use an N-channel logic-level MOSFET (like 2N7000 or AO3400) or a Darlington pair.