At this first picture i have a NPN transistor with Beta=75, 2N222A transistor, both Inputs are 5V. it was very simple to calculate the current that will flow through the LED. as it is simply I1 * Beta = I2, and I3 = I1+I2.
But if i replace it with a resistor of value 5k for example the I1*B = I2 relationship is not valid anymore.
My question is, I1*Beta = Maximum I2 current, would that be a better explanation of a relationship or i don't understand something ?