An open switch is not a conducting edge, so the loop current is zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

An open switch breaks the path

When the switch is open, the conducting loop is broken at the switch.

open switchno conducting loop\text{open switch} \Rightarrow \text{no conducting loop}
Open switch pathThe open switch leaves a gap in the loop.12 Vopen4 ohmA0 A

The current reading is zero

With no conducting path, the ammeter reads 0 amperes.

I=0 AI = 0\ \text{A}
Open switch pathThe open switch leaves a gap in the loop.12 Vopen4 ohmA0 A

Voltage does not matter without a path

The open switch blocks the branch in every row. Changing source voltage or load resistance does not create a conducting loop.

VRI6 V3 ohm0 A12 V4 ohm0 A18 V6 ohm0 A\begin{array}{c|c|c}V&R&I\\6\ \text{V}&3\ \text{ohm}&0\ \text{A}\\12\ \text{V}&4\ \text{ohm}&0\ \text{A}\\18\ \text{V}&6\ \text{ohm}&0\ \text{A}\\\end{array}
Open switch pathThe middle table row is the checked open diagram.12 Vopen4 ohmA0 A