The tendency to think primarily in terms of voltage is, I think, the greatest cause of confusion for anyone new to electronics. Once you develop an understanding of current everything will start to fall into place including the voltages. If, for instance, you need to analyse a transistor circuit the first step is to calculate the currents and from there you work out the voltages. If you try to establish voltages first; you will, in most cases, struggle to see what's going.

 

The reason I started this thread was because I could not answer this question: Why does a larger resistor at the base leg cause an LED on the other side of a transistor to shine brighter?

After watching the video lecture about transistors from my physics class again and experimenting with the circuit on a breadboard, I understand the answer now. When the switch is closed, as the value of the resistor R3 increases, the transistor acts more and more as if it was off and the switch was open. So for example, if R3=1MegΩ, the transistor is only half as effective as it was when R3 was smaller, and the LED does shine, but only dimly.

If I can get this question answered, then I'll be happy with my knowledge about transistors for now.

So now I'm happy, and I'll put this thread to bed.

EDIT: For future reference, I found this post helpful to explain the basics of how NPN transistors work.