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Bipolar Junction Transistor Operatingoperating modes

If I use the Bjta BJT transistor as a switch, the transistor operates in the saturation or cut-off region, not in the active region. 
However, some sources use the formula IcIC = B*Ibβ·IB. However, this formula is only used if the transistor is in the active region. So what's wrong?

Second question: If I connect a very large resistor (1M ohm1 MΩ) or a very small resistor (1m ohm1 mΩ) to the collector, will it still produce the same current according to this formula?

Third question: What exactly should I do to bring this transistor into these modes?

Bipolar Junction Transistor Operating modes

If I use the Bjt transistor as a switch, the transistor operates in the saturation or cut-off region, not in the active region. However, some sources use the formula Ic = B*Ib. However, this formula is only used if the transistor is in the active region. So what's wrong?

Second question: If I connect a very large resistor (1M ohm) or a very small resistor (1m ohm) to the collector, will it still produce the same current according to this formula?

Third question: What exactly should I do to bring this transistor into these modes?

Bipolar Junction Transistor operating modes

If I use a BJT transistor as a switch, the transistor operates in the saturation or cut-off region, not in the active region. 
However, some sources use the formula IC = β·IB. However, this formula is only used if the transistor is in the active region. So what's wrong?

Second question: If I connect a very large resistor (1 MΩ) or a very small resistor (1 mΩ) to the collector, will it still produce the same current according to this formula?

Third question: What exactly should I do to bring this transistor into these modes?

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Bipolar Junction Transistor Operating modes

If I use the Bjt transistor as a switch, the transistor operates in the saturation or cut-off region, not in the active region. However, some sources use the formula Ic = B*Ib. However, this formula is only used if the transistor is in the active region. So what's wrong?

Second question: If I connect a very large resistor (1M ohm) or a very small resistor (1m ohm) to the collector, will it still produce the same current according to this formula?

Third question: What exactly should I do to bring this transistor into these modes?