Q5: Through which resistor is there always a current flowing, regardless of the position of the switches?

The current leaves the positive terminal of $V_S$ and goes through switch SW1. Switch SW1 can connect to any of the resistors $R_1, R_2, R_3,$ or $R_4$. Regardless of which position SW1 is in (1, 2, 3, or 4), current will flow through one of these resistors to a common node.

From this common node, the current has two possible paths to ground:

• Through resistor $R_5$, which is directly connected between the common node and ground.
• Through switch SW2 and then resistor $R_6$.

Since SW1 must always be in one of its four positions, there will always be a voltage at the common node. Resistor $R_5$ is directly connected between this common node and ground, forming a complete circuit path. Therefore, current will always flow through $R_5$.
Current will only flow through $R_6$ if switch SW2 is closed. If SW2 is open, no current flows through $R_6$.

The resistor through which there is always a current flowing, regardless of the position of the switches, is \boxed{\text{R_5}}.

Q6: Determine the total resistance voltage at points A, B, and C in the circuit and the current through R4.

To solve this question, the following information is needed but not provided in the image:

• The numerical values for the voltage source $V_S$ and all resistors ($R_1, R_2, R_3, R_4, R_5, R_6$).
• The specific locations of points A, B, and C in the circuit diagram.
• The positions of switches SW1 and SW2 (e.g., which resistor SW1 is connected to, and whether SW2 is open or closed).

Without this essential information, it is not possible to calculate the total resistance, voltages at points A, B, C, or the current through $R_4$.