Doing any calculation in this type of a circuit is not a easy job. Why ? Because we have too many unknowns.
But we could try assume some and this might help us.
First let us assume that the LED will light if Id >1mA and the transistor current gain is Hfe = 150 and Vbe_on >0.6V.
To get 1mA or larger at collector we need Ib > 1mA/150 = 6.6μA.
And If Vcc = 5V and R1 = 100kΩ the LED will start to light if Rldr is larger than
Rldr > 0.6V/((5V - 0.6V)/100k - 6.6μA) = 16kΩ.
So the BJT is turn ON and its work on active region (Ic = hfe*Ib).
But as Rldr resistance increase (the sun light is getting weaker), more current from R1 can now flow into the transistor base. And this will increase Ic current (Ic = Hfe*Ib), larger collector current will cause more voltage drop across Rc resistor. And this will drop the voltage at collector. And when this voltage reach 0.6V the transistor is on the edge between active region and saturation.
And this will happens if Rldr is larger than:
Ic = (Vcc - Vd - Vce)/Rc = (5V - 2V - 0.6V)/680Ω = 3.5mA
Ib = 3.5mA/150 ≈ 24μA
And new Vbe value is 26mV*ln(24/6.6) + 0.6V = 0.635V
Rldr > 0.635V/((5V - 0.635V)/100k - 24μA) = 32kΩ
And this means that if Rldr is >> 32kΩ the BJT will be in saturation (Full-ON) and the Ic current reach his maximum value.
Ic_max = (Vcc - Vd - Vce(sat))/Rc = (5V - 2V - 0.2V)/680Ω = 4.1mA
And the LED is also at the maximum brightness
As for BJT. The transistor will be in cut-off if Vbe < 0.5V for a ordinary small-signal BJT.
http://forum.allaboutcircuits.com/threads/npn-base-resistor.97834/page-2#post-731057
As for the saturation try read this
http://forum.allaboutcircuits.com/threads/bjt-saturation-question-s.81150/#post-577296
http://forum.allaboutcircuits.com/threads/which-method-npn.97963/#post-731172
But we could try assume some and this might help us.
First let us assume that the LED will light if Id >1mA and the transistor current gain is Hfe = 150 and Vbe_on >0.6V.
To get 1mA or larger at collector we need Ib > 1mA/150 = 6.6μA.
And If Vcc = 5V and R1 = 100kΩ the LED will start to light if Rldr is larger than
Rldr > 0.6V/((5V - 0.6V)/100k - 6.6μA) = 16kΩ.
So the BJT is turn ON and its work on active region (Ic = hfe*Ib).
But as Rldr resistance increase (the sun light is getting weaker), more current from R1 can now flow into the transistor base. And this will increase Ic current (Ic = Hfe*Ib), larger collector current will cause more voltage drop across Rc resistor. And this will drop the voltage at collector. And when this voltage reach 0.6V the transistor is on the edge between active region and saturation.
And this will happens if Rldr is larger than:
Ic = (Vcc - Vd - Vce)/Rc = (5V - 2V - 0.6V)/680Ω = 3.5mA
Ib = 3.5mA/150 ≈ 24μA
And new Vbe value is 26mV*ln(24/6.6) + 0.6V = 0.635V
Rldr > 0.635V/((5V - 0.635V)/100k - 24μA) = 32kΩ
And this means that if Rldr is >> 32kΩ the BJT will be in saturation (Full-ON) and the Ic current reach his maximum value.
Ic_max = (Vcc - Vd - Vce(sat))/Rc = (5V - 2V - 0.2V)/680Ω = 4.1mA
And the LED is also at the maximum brightness
As for BJT. The transistor will be in cut-off if Vbe < 0.5V for a ordinary small-signal BJT.
http://forum.allaboutcircuits.com/threads/npn-base-resistor.97834/page-2#post-731057
As for the saturation try read this
http://forum.allaboutcircuits.com/threads/bjt-saturation-question-s.81150/#post-577296
http://forum.allaboutcircuits.com/threads/which-method-npn.97963/#post-731172
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