Ideal Transistor Switch

A bipolar transistor can be made to approximate an ideal switch.
Consider a common emitter transistor circuit,

A collector resistance R_C is connected from the transistor collector to the supply voltage V_CC.
The emitter terminal of the device is grounded.
For the transistor to simulate a switch, the terminals of the switch are the transistor collector and emitter.
The input voltage or the controlling voltage for the transistor switch is the base-emitter voltage V_BE.
The collector-emitter voltage V_CE is equal to the supply voltage minus the voltage drop across R_C,

V_CE=V_CC-I_CR_C

When the transistor base-emitter voltage is zero or reverse biased, the base current I_B is zero, and the collector current I_C is also zero. The transistor switch is now in its OFF condition.

Since there is no collector current, there can be no voltage drop across the load resistor.
Therefore when I_C=0,

V_CE=V_CC

Thus, when an ideal transistor switch is OFF, its collector-emitter voltage equals the supply voltage.

When the transistor base is made positive with respect to the emitter, a base current I_B flows. The collector current I_C is equal to I_B multiplied by the transistor common-emitter dc current gain h_FE.
i.e.  I_C=h_FE*I_B 
If I_B is made large enough, I_CR_C can become equal to the supply voltage V_CC.

Therefore,

V_CE=V_CC-V_CC=0

Thus, when an ideal transistor switch is ON, its collector-emitter voltage equals zero.

Ideally, it dissipates zero power when ON or OFF.
Transistor power dissipation is given by,

P_D=I_CV_CE

When the switch is OFF, I_C=0,

P_D=0

When the switch is ON, V_CE=0,

P_D=0

The only time power is dissipated is when the device is switching between ON and OFF.