Electrical – Why the resistor is not considered

I'm not going to just give you the answer to your homework problem.

However, consider what it really means to be a voltage source. Let's say I have a 6V source that is good to 1 A. What voltage is it when nothing is connected? When I put a 60 Ω resistor accross it? A 30 Ω resistor accross it?

If I put the 6 V source and resistor inside a black box and brought out only the two leads, what difference could someone observe on the outside to distinguish the no load, 60 Ω and 30 Ω cases? Now consider this is the case you have. Your +6V and R are inside the box and the rest of the circuit on the outside.

This is so because the voltage source is ideal, and therefore, deliver a constant voltage, regardless of current requested.

The effect of adding a resistor in parallel to the voltage source, is to ask more current, which does not affect the source voltage.

For example, consider this simple circuit:

^{simulate this circuit – Schematic created using CircuitLab}

Does it depend on the current through \$R_4\$, the value of \$R_1\$? Of course not. Moreover, one can remove the resistor \$R_1\$ and the current circuit by \$R_4\$ be the same. \$R_1\$ does affect the amount of current that requests the V1 source, but as this source is ideal, the voltage applied to the set \$R_2\$, \$R_3\$ and \$R_4\$ is unchanged.

Another way to look at it is considering that the voltage source is an element that imposes the voltage between two nodes, regardless of other elements (passive element) are connected between the two nodes. That's why, for example, you can not connect two voltage sources in parallel, since a singularity is generated.