I'm currently studying the textbook Fundamentals of Electric Circuits, 7th edition, by Charles Alexander and Matthew Sadiku. Chapter 1.7 Problem Solving gives the following example:

Example 1.10

Solve for the current flowing through the \$8 \ \Omega\$ resistor in Fig. 1.19.

Solution:

1. Carefully define the problem. This is only a simple example, but we can already see that we do not know the polarity on the 3-V source. We have the following options. We can ask the professor what the polarity should be. If we cannot ask, then we need to make a decision on what to do next. If we have time to work the problem both ways, we can solve for the current when the 3-V source is plus on top and then plus on the bottom. If we do not have the time to work it both ways, assume a polarity and then carefully document your decision. Let us assume that the professor tells us that the source is plus on the bottom as shown in Fig. 1.20.

Notice that the authors have claimed (without justification) that the current is flowing downwards through the \$8 \ \Omega\$ resistor. In SpiRail's answer here, they have also shown that, for the case where the polarity is + on the bottom, the current flows downwards through the \$8 \ \Omega\$ resistor (see the red arrow): How does one know that the current is flowing downwards through the \$8 \ \Omega\$ resistor? This seems to be the immediate assumption, but there's no explanation from the authors as to why this is the case.

I'm currently studying the textbook Fundamentals of Electric Circuits, 7th edition, by Charles Alexander and Matthew Sadiku. Chapter 1.7 Problem Solving gives the following example:

Example 1.10

Solve for the current flowing through the \$8 \ \Omega\$ resistor in Fig. 1.19.

Solution:

1. Carefully define the problem. This is only a simple example, but we can already see that we do not know the polarity on the 3-V source. We have the following options. We can ask the professor what the polarity should be. If we cannot ask, then we need to make a decision on what to do next. If we have time to work the problem both ways, we can solve for the current when the 3-V source is plus on top and then plus on the bottom. If we do not have the time to work it both ways, assume a polarity and then carefully document your decision. Let us assume that the professor tells us that the source is plus on the bottom as shown in Fig. 1.20.

Notice that the authors have claimed (without justification) that the current is flowing downwards through the \$8 \ \Omega\$ resistor. In SpiRail's answer here, they have also shown that, for the case where the polarity is + on the bottom, the current flows downwards through the \$8 \ \Omega\$ resistor (see the red arrow): How does one know that the current is flowing downwards through the \$8 \ \Omega\$ resistor? This seems to be the immediate assumption, but there's no explanation from the authors as to why this is the case.