Question

evaluation and review questions: 1. why doesnt the starting point for summing the voltages around a closed loop make any difference? 2. kirchhoffs voltage law applies to any closed path, even one without current. how did the result of step 9 show that this is true? 3. based on the result you observed in step 9, what voltage would you expect in a 120 v circuit across an open (blown) fuse? 4. use kirchhoffs voltage law to find vx in figure 6 - 7.

Explanation:

Step1: Recall Kirchhoff's voltage law

Kirchhoff's voltage law (KVL) states that the sum of the electrical potential differences (voltages) around any closed network is zero, i.e., $\sum V = 0$. Since the sum of voltages in a closed - loop is a closed - path integral of the electric field, and the electric field is a conservative field. The value of a line integral of a conservative field around a closed path is independent of the starting point.

Step2: Analyze step - 9 result for KVL in a path without current

Without knowing the details of step 9, in general, for a closed path without current, the voltage drops across resistors (which are proportional to current $V = IR$) are zero. But there can still be emf sources in the loop. KVL holds as the sum of emf sources and any non - zero voltage drops (e.g., across capacitors if present) still sums to zero.

Step3: Determine voltage across a blown fuse

In a 120 V circuit, when a fuse is blown (open), the circuit is broken. The voltage across the open fuse is equal to the supply voltage, which is 120 V. This is because there is no current flowing through the circuit (open - circuit condition), and the potential difference across the open points is equal to the source voltage.

Step4: Apply KVL to find $V_x$

Let's assume a clock - wise loop. Starting from the bottom left corner and moving clock - wise, we have: $9 - 2-4 - V_x=0$. Rearranging the equation to solve for $V_x$ gives $V_x=9 - 2 - 4$.
$V_x = 3$ V

Answer:

1. Because the electric field is conservative and the sum of voltages in a closed - loop is a closed - path integral of the electric field.
2. Without details of step 9, in general, for a no - current closed path, KVL holds as the sum of emf sources and other non - zero voltage drops sums to zero.
3. 120 V
4. $V_x = 3$ V