I began to read up on transistors, which led me to this post on electronics stackexchange.
At the end of the original post, the question asks "the voltage at the base would be a sine wave with the DC bias as the baseline, correct?"
I understand the V2 with the two resistors in series is a voltage divider.
I am struggling to see how at the node connected to the base, the voltage is going to be simply the sum of V1 and V2, resulting in the AC signal superimposed on the DC signal from V2.
I think I can best express my confusion in the form of the second image below.
The voltage between the capacitor and GND is ground no matter the input oscillating voltage before the capacitor.
Then why should the first case be the sum of the AC from source 1 and DC from source 2 ?
Also, I remember playing with small batteries as a child. When I put hooked up those batteries of the same voltage in parallel, the voltage output was the same as having a single battery, which I believe is kind of like the first case. (So why should it be the sum of the two voltage sources in the case of the first image?)