Transistor as a switch:

Transistors are generally employed as electronic switches, for both of the high power applications including switched-mode power supplies and low power applications like logic gates.

In a grounded-emitter transistor circuit, like the light-switch circuit shown, as the base voltage increases the base and collector current rise exponentially, and the collector voltage drops due to the collector load resistor. The appropriate equations:

V_RC = I_CE × R_C, the voltage across the load (the lamp with resistance RC)

V_RC + V_CE = V_CC, the supply voltage shown as 6V

If V_CE could fall to 0 (perfect closed switch) after that the I_c could go no higher than V_CC / R_C, even along with higher base voltage and current. After that the transistor is said to be saturated. Therefore, values of input voltage can be selected such that the output is either totally off, or totally on. The transistor is acting like a switch, and this kind of operation is general in digital circuits in which only "on" and "off" values are relevant.